Quantum Reports

Research

12 pages, 2968 KiB

Open AccessArticle

Molecular Structure of M(N₁₃) Compounds with 12-Membered Nitrogen-Containing Cycle and Axial Nitrogen Atom (M = Mn, Fe): Quantum-Chemical Design by DFT Method

by Oleg V. Mikhailov and Denis V. Chachkov

Quantum Rep. 2023, 5(1), 282-293; https://doi.org/10.3390/quantum5010019 - 15 Mar 2023

Cited by 4 | Viewed by 1750

Abstract

Based on the results of a quantum chemical calculation using the DFT method in the B3PW91/TZVP, OPBE/TZVP, M06/TZVP, and M062/Def2TZVP levels, the possibility of the existence of M(N₁₃) chemical compounds (M = Mn, Fe) that are unknown for these elements has [...] Read more.

Based on the results of a quantum chemical calculation using the DFT method in the B3PW91/TZVP, OPBE/TZVP, M06/TZVP, and M062/Def2TZVP levels, the possibility of the existence of M(N₁₃) chemical compounds (M = Mn, Fe) that are unknown for these elements has been predicted. Data on the structural parameters, the multiplicity of the ground state, APT and NBO analysis, and standard thermodynamic parameters of formation (standard enthalpy Δ_fH⁰, entropy S⁰, and Gibbs’s energy Δ_fG⁰) for these compounds are presented. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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15 pages, 479 KiB

Open AccessArticle

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

by Nathaniel Wrobel, Anshumitra Baul, Ka-Ming Tam and Juana Moreno

Quantum Rep. 2022, 4(4), 574-588; https://doi.org/10.3390/quantum4040042 - 8 Dec 2022

Viewed by 2643

Abstract

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical [...] Read more.

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point. Full article

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10 pages, 501 KiB

Open AccessArticle

Fricke Topological Qubits

by Michel Planat, David Chester, Marcelo M. Amaral and Klee Irwin

Quantum Rep. 2022, 4(4), 523-532; https://doi.org/10.3390/quantum4040037 - 14 Nov 2022

Cited by 4 | Viewed by 3892

Abstract

We recently proposed that topological quantum computing might be based on

S L (2, C)

representations of the fundamental group

π_{1} (S^{3} \ K)

for the complement of a link K in the three-sphere. The restriction [...] Read more.

We recently proposed that topological quantum computing might be based on

S L (2, C)

representations of the fundamental group

π_{1} (S^{3} \ K)

for the complement of a link K in the three-sphere. The restriction to links whose associated

S L (2, C)

character variety

V

contains a Fricke surface

κ_{d} = x y z - x^{2} - y^{2} - z^{2} + d

is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link

L 2 a 1

, one of the three arithmetic two-bridge links (the Whitehead link

5_{1}^{2}

, the Berge link

6_{2}^{2}

or the double-eight link

6_{3}^{2}

) or the link

7_{3}^{2}

, the

V

for those links contains the reducible component

κ_{4}

, the so-called Cayley cubic. In addition, the

V

for the latter two links contains the irreducible component

κ_{3}

, or

κ_{2}

, respectively. Taking

ρ

to be a representation with character

κ_{d}

(

d < 4

), with

| x |, | y |, | z | \leq 2

, then

ρ (π_{1})

fixes a unique point in the hyperbolic space

H_{3}

and is a conjugate to a

S U (2)

representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlevé VI equation. The 0-surgery on the three circles of the Borromean rings L6a4 is taken as an example. Full article

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8 pages, 314 KiB

Open AccessArticle

Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements

by Roberto Leporini and Davide Pastorello

Quantum Rep. 2022, 4(4), 434-441; https://doi.org/10.3390/quantum4040031 - 17 Oct 2022

Cited by 1 | Viewed by 1918

Abstract

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining [...] Read more.

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination. Full article

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17 pages, 348 KiB

Open AccessArticle

Coarse-Graining of Observables

by Stan Gudder

Quantum Rep. 2022, 4(4), 401-417; https://doi.org/10.3390/quantum4040029 - 3 Oct 2022

Cited by 1 | Viewed by 1584

Abstract

We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of a single probability measure. We [...] Read more.

We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of a single probability measure. We then show that any two probability measures coexist. We extend these concepts to observables and instruments and mention that two observables need not coexist. We define the discretization of an observable as a special case of coarse-graining and show that these have 0–1 stochastic kernels. We next consider finite observables and instruments and show that in these cases, stochastic kernels are replaced by stochastic matrices. We also show that coarse-graining is the same as post-processing in this finite case. We then consider sequential products of observables and discuss the sequential product of a post-processed observable with another observable. We briefly discuss SIC observables and the example of qubit observables. Full article

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17 pages, 3885 KiB

Open AccessArticle

Quantum Circuit Learning with Error Backpropagation Algorithm and Experimental Implementation

by Masaya Watabe, Kodai Shiba, Chih-Chieh Chen, Masaru Sogabe, Katsuyoshi Sakamoto and Tomah Sogabe

Quantum Rep. 2021, 3(2), 333-349; https://doi.org/10.3390/quantum3020021 - 28 May 2021

Cited by 9 | Viewed by 5062

Abstract

Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high-dimensional state or function approximation. Quantum–classical hybrid [...] Read more.

Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high-dimensional state or function approximation. Quantum–classical hybrid algorithms have been proposed in recent years for this purpose under the noisy intermediate-scale quantum computer (NISQ) environment. Under this scheme, the role played by the classical computer is the parameter tuning, parameter optimization, and parameter update for the quantum circuit. In this paper, we propose a gradient descent-based backpropagation algorithm that can efficiently calculate the gradient in parameter optimization and update the parameter for quantum circuit learning, which outperforms the current parameter search algorithms in terms of computing speed while presenting the same or even higher test accuracy. Meanwhile, the proposed theoretical scheme was successfully implemented on the 20-qubit quantum computer of IBM Q, ibmq_johannesburg. The experimental results reveal that the gate error, especially the CNOT gate error, strongly affects the derived gradient accuracy. The regression accuracy performed on the IBM Q becomes lower with the increase in the number of measurement shot times due to the accumulated gate noise error. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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14 pages, 342 KiB

Open AccessArticle

The ABC of Deutsch–Hayden Descriptors

by Charles Alexandre Bédard

Quantum Rep. 2021, 3(2), 272-285; https://doi.org/10.3390/quantum3020017 - 27 Apr 2021

Cited by 8 | Viewed by 4017

Abstract

It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum [...] Read more.

It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors. Full article

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14 pages, 587 KiB

Open AccessArticle

Remote State Design for Efficient Quantum Metrology with Separable and Non-Teleporting States

by Rahul Raj, Shreya Banerjee and Prasanta K. Panigrahi

Quantum Rep. 2021, 3(1), 228-241; https://doi.org/10.3390/quantum3010013 - 9 Mar 2021

Cited by 3 | Viewed by 3315

Abstract

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by [...] Read more.

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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23 pages, 528 KiB

Open AccessArticle

Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems

by Isabel Sainz, Andrés García and Andrei B. Klimov

Quantum Rep. 2021, 3(1), 173-195; https://doi.org/10.3390/quantum3010011 - 27 Feb 2021

Cited by 3 | Viewed by 2949

Abstract

We analyze periodically modulated quantum systems with

S U (2)

and

S U (1, 1)

symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions [...] Read more.

We analyze periodically modulated quantum systems with

S U (2)

and

S U (1, 1)

symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities. Full article

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7 pages, 290 KiB

Open AccessArticle

Spectral Explanation for Statistical Odd-Even Staggering in Few Fermions Systems

by Angelo Plastino, Gustavo Luis Ferri and Angel Ricardo Plastino

Quantum Rep. 2021, 3(1), 166-172; https://doi.org/10.3390/quantum3010010 - 16 Feb 2021

Cited by 5 | Viewed by 2584

Abstract

Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as for example, ultra small metallic grains [...] Read more.

Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as for example, ultra small metallic grains and metal clusters. We work in this effort with the above-mentioned Lipkin-like, two-level fermion model and show that statistical staggering effects can be detailedly explained by recourse to a straightforward analysis of the associated energy-spectra. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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16 pages, 1287 KiB

Open AccessArticle

Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates

by Pejman Jouzdani and Stefan Bringuier

Quantum Rep. 2021, 3(1), 137-152; https://doi.org/10.3390/quantum3010008 - 31 Jan 2021

Cited by 2 | Viewed by 4206

Abstract

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting [...] Read more.

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH₂ and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H₂ molecule. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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15 pages, 739 KiB

Open AccessArticle

How to Erase Quantum Monogamy?

by Ghenadie Mardari

Quantum Rep. 2021, 3(1), 53-67; https://doi.org/10.3390/quantum3010004 - 21 Jan 2021

Cited by 1 | Viewed by 3358

Abstract

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact [...] Read more.

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured in a delayed-choice arrangement. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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11 pages, 738 KiB

Open AccessArticle

Superradiance in Quantum Vacuum

by José Tito Mendonça

Quantum Rep. 2021, 3(1), 42-52; https://doi.org/10.3390/quantum3010003 - 3 Jan 2021

Cited by 3 | Viewed by 3358

Abstract

A new process associated with the nonlinear optical properties of the electromagnetic quantum vacuum is described. It corresponds to the superradiant emission of photons, resulting from the interaction of an intense laser pulse with frequency

ω_{0}

with a counter-propagating high-harmonic signal with [...] Read more.

A new process associated with the nonlinear optical properties of the electromagnetic quantum vacuum is described. It corresponds to the superradiant emission of photons, resulting from the interaction of an intense laser pulse with frequency

ω_{0}

with a counter-propagating high-harmonic signal with a spectrum of frequencies

n ω_{1}

, for n integer, in the absence of matter. Under certain conditions, photon emission from vacuum will be enhanced by the square of the number of intense spikes associated with the high-harmonic pulse. This occurs when the field created by the successive spikes is coherently emitted, as in typical superradiant processes involving atoms. Subradiant conditions, where the nonlinearity of quantum vacuum is entirely suppressed, can equally be defined. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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29 pages, 617 KiB

Open AccessArticle

Spacetime Paths as a Whole

by Sky Nelson-Isaacs

Quantum Rep. 2021, 3(1), 13-41; https://doi.org/10.3390/quantum3010002 - 31 Dec 2020

Cited by 1 | Viewed by 6566

Abstract

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman’s original derivation of the [...] Read more.

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman’s original derivation of the path integral formulation of non-relativistic quantum mechanics uses time-slicing to calculate amplitudes as sums over all possible paths through space, but along a definite curve through time. Here, a 3+1D spacetime wave distribution and its 4-momentum dual are formally developed which have no external time parameter and therefore cannot change or evolve in the usual sense. Time is thus seen “from the outside”. A given 3+1D momentum representation of a system encodes complete dynamical information, describing the system’s spacetime behavior as a whole. A comparison is made to the mathematics of holograms, and properties of motion for simple systems are derived. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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12 pages, 1455 KiB

Open AccessArticle

Tunable Topological Beam Splitter in Superconducting Circuit Lattice

by Lu Qi, Yan Xing, Xue-Dong Zhao, Shutian Liu, Xue Han, Wen-Xue Cui, Shou Zhang and Hong-Fu Wang

Quantum Rep. 2021, 3(1), 1-12; https://doi.org/10.3390/quantum3010001 - 25 Dec 2020

Cited by 4 | Viewed by 3686

Abstract

In the usual Su–Schrieffer–Heeger (SSH) model with an even number of lattice sites, the topological pumping between left and right edge states cannot be easily realized since the edge states occupy two-end sites simultaneously. Here we propose a scheme to investigate the topological [...] Read more.

In the usual Su–Schrieffer–Heeger (SSH) model with an even number of lattice sites, the topological pumping between left and right edge states cannot be easily realized since the edge states occupy two-end sites simultaneously. Here we propose a scheme to investigate the topological edge pumping in an even-sized periodically modulated SSH model mapped by a one dimensional superconducting transmission line resonators array. We find that the photon initially prepared in the first resonator can be finally observed at the two-end resonators with a certain proportion. The final photon splitting at the two-end resonators indicates that the present superconducting circuit is expected to realize the topological beam splitter. Further, we demonstrate that the splitting proportion between the two-end resonators can be arbitrarily tuned from 1 to 0, implying the potential feasibility of implementing the tunable topological beam splitter. Meanwhile, we also show that the tunable topological beam splitter is immune to the mild disorder added into the system due to the topology protection of the zero energy modes, and find that the tunable topological beam splitter is much more robust to the global on-site disorder compared with the nearest neighbor disorder. Our work greatly extends the practical application of topological matter in quantum information processing and opens up a new way towards the engineering of topological quantum optical device. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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17 pages, 370 KiB

Open AccessArticle

Classical Logic in the Quantum Context

by Andrea Oldofredi

Quantum Rep. 2020, 2(4), 600-616; https://doi.org/10.3390/quantum2040042 - 5 Dec 2020

Cited by 2 | Viewed by 3880

Abstract

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every [...] Read more.

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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19 pages, 481 KiB

Open AccessArticle

Higher-Order Information Measures from Cumulative Densities in Continuous Variable Quantum Systems

by Saúl J. C. Salazar, Humberto G. Laguna and Robin P. Sagar

Quantum Rep. 2020, 2(4), 560-578; https://doi.org/10.3390/quantum2040039 - 6 Nov 2020

Cited by 4 | Viewed by 3636

Abstract

A definition of three-variable cumulative residual entropy is introduced, and then used to obtain expressions for higher order or triple-wise correlation measures, that are based on cumulative residual densities. These information measures are calculated in continuous variable quantum systems comprised of three oscillators, [...] Read more.

A definition of three-variable cumulative residual entropy is introduced, and then used to obtain expressions for higher order or triple-wise correlation measures, that are based on cumulative residual densities. These information measures are calculated in continuous variable quantum systems comprised of three oscillators, and their behaviour compared to the analogous measures from Shannon information theory. There is an overall consistency in the behaviour of the newly introduced measures as compared to the Shannon ones. There are, however, differences in interpretation, in the case of three uncoupled oscillators, where the correlation is due to wave function symmetry. In interacting systems, the cumulative based measures are shown in order to detect salient features, which are also present in the Shannon based ones. Full article

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18 pages, 1007 KiB

Open AccessArticle

Violation of Bell-CHSH Inequalities through Optimal Local Filters in the Vacuum

by Akira Matsumura and Yasusada Nambu

Quantum Rep. 2020, 2(4), 542-559; https://doi.org/10.3390/quantum2040038 - 5 Nov 2020

Cited by 4 | Viewed by 2954

Abstract

We investigate quantum correlations appearing for two-qubit detectors which are initially uncorrelated and locally coupled to a massless scalar field in a vacuum state. Under the perturbation up to the second order in the coupling, the state of the detectors can be entangled [...] Read more.

We investigate quantum correlations appearing for two-qubit detectors which are initially uncorrelated and locally coupled to a massless scalar field in a vacuum state. Under the perturbation up to the second order in the coupling, the state of the detectors can be entangled through the interaction with the scalar field but satisfies the Bell-CHSH inequality. The violation of the Bell-CHSH inequality for such an entangled state is revealed by local filtering operations. In this paper, we construct the optimal filtering operations for the qubit detectors and derive the success probability of the filtering. The success probability characterizes the reliability of revealing the violation of the Bell-CHSH inequality by the filtering operations. Through these analyses, we demonstrate a trade-off relation between the success probability and the size of parameter region showing the violation of the Bell-CHSH inequality. Full article

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13 pages, 602 KiB

Open AccessArticle

Temperature-Fermion Number Correlations in Finite Paired Systems

by Angelo Plastino, Diana Monteoliva and Angel R. Plastino

Quantum Rep. 2020, 2(4), 529-541; https://doi.org/10.3390/quantum2040037 - 5 Nov 2020

Viewed by 2463

Abstract

We investigate finite systems of N paired fermions, common in atomic nuclei, for example. These systems exhibit quantum mechanical features akin to those of superconductors. We discover, however, some specific N dependent effects that can not be attained in the thermodynamics limit of [...] Read more.

We investigate finite systems of N paired fermions, common in atomic nuclei, for example. These systems exhibit quantum mechanical features akin to those of superconductors. We discover, however, some specific N dependent effects that can not be attained in the thermodynamics limit of ordinary superconductivity. In particular, an important fact is uncovered: there is a strong correlation between the temperature T and the number of fermions N. A certain temperature increase

Δ T

produces, in thermal quantifiers (such as the entropy), quite different effects if

N = 4

or

N = 25

. In fact, whether a given temperature value should be regarded as high or low can not be ascertained independent of the N value. Full article

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13 pages, 365 KiB

Open AccessArticle

Generalizing Wave-Particle Duality: Two-Qubit Extension of the Polarization Coherence Theorem

by Francisco De Zela

Quantum Rep. 2020, 2(4), 501-513; https://doi.org/10.3390/quantum2040035 - 26 Oct 2020

Cited by 5 | Viewed by 3425

Abstract

We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT:

V^{2} + D^{2} = P^{2}

, involves three measures, visibility

V

, distinguishability [...] Read more.

We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT:

V^{2} + D^{2} = P^{2}

, involves three measures, visibility

V

, distinguishability

D

, and the degree of polarization

P

, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT:

V^{2} + D^{2} \leq 1

, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects. Full article

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28 pages, 1059 KiB

Open AccessArticle

“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

by Theodoros Pailas

Quantum Rep. 2020, 2(3), 414-441; https://doi.org/10.3390/quantum2030029 - 7 Aug 2020

Cited by 3 | Viewed by 3399

Abstract

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the [...] Read more.

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance

r \to f (\tilde{r})

. As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac’s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is “more” or “less” singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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9 pages, 693 KiB

Open AccessArticle

Generation of Entanglement between Two Two-Level Atoms Coupled to a Microtoroidal Cavity Via Thermal Field

by Emilio H. S. Sousa and J. A. Roversi

Quantum Rep. 2020, 2(3), 343-351; https://doi.org/10.3390/quantum2030024 - 8 Jul 2020

Cited by 1 | Viewed by 3038

Abstract

We investigate the entanglement dynamics of a system comprising a pair of two-level dipole-dipole interacting atoms coupled to a microtoroidal resonator. Each atom is individually coupled with the two counter-propagating whispering gallery modes of the resonator through their evanescent fields. The atom-atom entanglement [...] Read more.

We investigate the entanglement dynamics of a system comprising a pair of two-level dipole-dipole interacting atoms coupled to a microtoroidal resonator. Each atom is individually coupled with the two counter-propagating whispering gallery modes of the resonator through their evanescent fields. The atom-atom entanglement shown for several parameter sets of the system was obtained using the negativity. For ideal resonators, it is seen that the entanglement is correlated to the dipole-dipole interaction and the average number of photons when the modes of the resonator are prepared in a thermal state even at high temperatures. Further, for the non-ideal resonator case, where there is a small structural deformation of the microtoroidal structure that allows a direct coupling between the modes, a counter-intuitive result is presented. The imperfections also offer the advantage of generating maximally entangled states for a two-atom subsystem with maximum fidelity. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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6 pages, 242 KiB

Open AccessArticle

Undecidable, Unrecognizable, and Quantum Computing

by Michael Siomau

Quantum Rep. 2020, 2(3), 337-342; https://doi.org/10.3390/quantum2030023 - 1 Jul 2020

Cited by 1 | Viewed by 4154

Abstract

Quantum computing allows us to solve some problems much faster than existing classical algorithms. Yet, the quantum computer has been believed to be no more powerful than the most general computing model—the Turing machine. Undecidable problems, such as the halting problem, and unrecognizable [...] Read more.

Quantum computing allows us to solve some problems much faster than existing classical algorithms. Yet, the quantum computer has been believed to be no more powerful than the most general computing model—the Turing machine. Undecidable problems, such as the halting problem, and unrecognizable inputs, such as the real numbers, are beyond the theoretical limit of the Turing machine. I suggest a model for a quantum computer, which is less general than the Turing machine, but may solve the halting problem for any task programmable on it. Moreover, inputs unrecognizable by the Turing machine can be recognized by the model, thus breaking the theoretical limit for a computational task. A quantum computer is not just a successful design of the Turing machine as it is widely perceived now, but is a different, less general but more powerful model for computing, the practical realization of which may need different strategies than those in use now. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

12 pages, 562 KiB

Open AccessArticle

Measurement-Based Adaptation Protocol with Quantum Reinforcement Learning in a Rigetti Quantum Computer

by Julio Olivares-Sánchez, Jorge Casanova, Enrique Solano and Lucas Lamata

Quantum Rep. 2020, 2(2), 293-304; https://doi.org/10.3390/quantum2020019 - 19 May 2020

Cited by 9 | Viewed by 3963

Abstract

We present an experimental realisation of a measurement-based adaptation protocol with quantum reinforcement learning in a Rigetti cloud quantum computer. The experiment in this few-qubit superconducting chip faithfully reproduces the theoretical proposal, setting the first steps towards a semiautonomous quantum agent. This experiment [...] Read more.

We present an experimental realisation of a measurement-based adaptation protocol with quantum reinforcement learning in a Rigetti cloud quantum computer. The experiment in this few-qubit superconducting chip faithfully reproduces the theoretical proposal, setting the first steps towards a semiautonomous quantum agent. This experiment paves the way towards quantum reinforcement learning with superconducting circuits. Full article

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15 pages, 377 KiB

Open AccessArticle

Classical Predictions for Intertwined Quantum Observables Are Contingent and Thus Inconclusive

by Karl Svozil

Quantum Rep. 2020, 2(2), 278-292; https://doi.org/10.3390/quantum2020018 - 13 May 2020

Cited by 9 | Viewed by 3364

Abstract

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (also known as gadgets) deliver the strongest form of classical value indefiniteness. However, the [...] Read more.

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (also known as gadgets) deliver the strongest form of classical value indefiniteness. However, the choice of the respective configuration among all such collections, and thus the relation of its terminals, remains arbitrary and cannot be motivated by some superselection principle inherent to quantum or classical physics. Full article

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Review

Jump to: Research, Other

23 pages, 452 KiB

Open AccessReview

Some Classical Models of Particles and Quantum Gauge Theories

by Andrey Akhmeteli

Quantum Rep. 2022, 4(4), 486-508; https://doi.org/10.3390/quantum4040035 - 3 Nov 2022

Cited by 1 | Viewed by 2558

Abstract

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described [...] Read more.

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative. Full article

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30 pages, 2279 KiB

Open AccessReview

Evidence of Predictive Power and Experimental Relevance of Weak-Values Theory

by C. Aris Chatzidimitriou-Dreismann

Quantum Rep. 2021, 3(2), 286-315; https://doi.org/10.3390/quantum3020018 - 4 May 2021

Cited by 3 | Viewed by 3001

Abstract

The concepts of Weak Values (WV) and Two-State Vector Formalism (TSVF) appear to motivate new experiments and to offer novel insights into dynamical processes in various materials of several scientific and technological fields. To support this view, here we consider the dynamics of [...] Read more.

The concepts of Weak Values (WV) and Two-State Vector Formalism (TSVF) appear to motivate new experiments and to offer novel insights into dynamical processes in various materials of several scientific and technological fields. To support this view, here we consider the dynamics of hydrogen atoms and/or molecules in nanostructured materials like e.g., carbon nanotubes. The experimental method applied is incoherent scattering of thermal (i.e., non-relativistic) neutrons (INS). In short, the main finding consists in the following effect: the measured energy and momentum transfers are shown to contradict even qualitatively the associated expectations of conventional scattering theory. This effect was recently observed in INS experiments, e.g., in H

_{2}

adsorbed in carbon nanotubes, where a large momentum transfer deficit was found. Due to the broad abundance of hydrogen, these findings may be also of technological importance, since they indicate a considerably enhanced H mobility in specific structured material environments. A new INS experiment is proposed concerning the H mobility of an ultra-fast proton conductor (H

_{3}

OSbTeO

_{6}

) being of technological relevance. Further neutron scattering investigations on other systems (metallic hydrides and H

_{2}

encapsulated inside C

_{60}

) are proposed. As concerns theoretical implications, the analysis of the experimental results strongly supports the view that the wavefunction (or state vector) represents an ontological physical entity of a single quantum system. Full article

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48 pages, 7908 KiB

Open AccessReview

Quantum Biology: An Update and Perspective

by Youngchan Kim, Federico Bertagna, Edeline M. D’Souza, Derren J. Heyes, Linus O. Johannissen, Eveliny T. Nery, Antonio Pantelias, Alejandro Sanchez-Pedreño Jimenez, Louie Slocombe, Michael G. Spencer, Jim Al-Khalili, Gregory S. Engel, Sam Hay, Suzanne M. Hingley-Wilson, Kamalan Jeevaratnam, Alex R. Jones, Daniel R. Kattnig, Rebecca Lewis, Marco Sacchi, Nigel S. Scrutton, S. Ravi P. Silva and Johnjoe McFadden Show full author list Hide full author list

Quantum Rep. 2021, 3(1), 80-126; https://doi.org/10.3390/quantum3010006 - 26 Jan 2021

Cited by 99 | Viewed by 31088

Abstract

Understanding the rules of life is one of the most important scientific endeavours and has revolutionised both biology and biotechnology. Remarkable advances in observation techniques allow us to investigate a broad range of complex and dynamic biological processes in which living systems could [...] Read more.

Understanding the rules of life is one of the most important scientific endeavours and has revolutionised both biology and biotechnology. Remarkable advances in observation techniques allow us to investigate a broad range of complex and dynamic biological processes in which living systems could exploit quantum behaviour to enhance and regulate biological functions. Recent evidence suggests that these non-trivial quantum mechanical effects may play a crucial role in maintaining the non-equilibrium state of biomolecular systems. Quantum biology is the study of such quantum aspects of living systems. In this review, we summarise the latest progress in quantum biology, including the areas of enzyme-catalysed reactions, photosynthesis, spin-dependent reactions, DNA, fluorescent proteins, and ion channels. Many of these results are expected to be fundamental building blocks towards understanding the rules of life. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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Other

Jump to: Research, Review

9 pages, 2362 KiB

Open AccessLetter

Avalanche Photodetector Based on InAs/InSb Superlattice

by Arash Dehzangi, Jiakai Li, Lakshay Gautam and Manijeh Razeghi

Quantum Rep. 2020, 2(4), 591-599; https://doi.org/10.3390/quantum2040041 - 4 Dec 2020

Cited by 18 | Viewed by 5263

Abstract

This work demonstrates a mid-wavelength infrared InAs/InSb superlattice avalanche photodiode (APD). The superlattice APD structure was grown by molecular beam epitaxy on GaSb substrate. The device exhibits a 100 % cut-off wavelength of 4.6 µm at 150 K and 4.30 µm at 77 [...] Read more.

This work demonstrates a mid-wavelength infrared InAs/InSb superlattice avalanche photodiode (APD). The superlattice APD structure was grown by molecular beam epitaxy on GaSb substrate. The device exhibits a 100 % cut-off wavelength of 4.6 µm at 150 K and 4.30 µm at 77 K. At 150 and 77 K, the device responsivity reaches peak values of 2.49 and 2.32 A/W at 3.75 µm under −1.0 V applied bias, respectively. The device reveals an electron dominated avalanching mechanism with a gain value of 6 at 150 K and 7.4 at 77 K which was observed under −6.5 V bias voltage. The gain value was measured at different temperatures and different diode sizes. The electron and hole impact ionization coefficients were calculated and compared to give a better prospect of the performance of the device. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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