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Quantum Rep., Volume 3, Issue 3 (September 2021) – 16 articles

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Article
Quantum Holography from Fermion Fields
Quantum Rep. 2021, 3(3), 576-591; https://doi.org/10.3390/quantum3030037 (registering DOI) - 19 Sep 2021
Viewed by 356
Abstract
In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields [...] Read more.
In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere. Full article
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Article
Bibliometric Analysis in the Field of Quantum Technology
Quantum Rep. 2021, 3(3), 549-575; https://doi.org/10.3390/quantum3030036 - 15 Sep 2021
Viewed by 403
Abstract
The second quantum technological revolution started around 1980 with the control of single quantum particles and their interaction on an individual basis. These experimental achievements enabled physicists, engineers, and computer scientists to utilize long-known quantum features—especially superposition and entanglement of single quantum states—for [...] Read more.
The second quantum technological revolution started around 1980 with the control of single quantum particles and their interaction on an individual basis. These experimental achievements enabled physicists, engineers, and computer scientists to utilize long-known quantum features—especially superposition and entanglement of single quantum states—for a whole range of practical applications. We use a publication set of 54,598 papers from Web of Science, published between 1980 and 2018, to investigate the time development of four main subfields of quantum technology in terms of numbers and shares of publications, as well as the occurrence of topics and their relation to the 25 top contributing countries. Three successive time periods are distinguished in the analyses by their short doubling times in relation to the whole Web of Science. The periods can be characterized by the publication of pioneering works, the exploration of research topics, and the maturing of quantum technology, respectively. Compared to the USA, China’s contribution to the worldwide publication output is overproportionate, but not in the segment of highly cited papers. Full article
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Article
The Measure Aspect of Quantum Uncertainty, of Entanglement, and the Associated Entropies
Quantum Rep. 2021, 3(3), 534-548; https://doi.org/10.3390/quantum3030035 - 12 Sep 2021
Viewed by 269
Abstract
Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting μ-uncertainties are described by [...] Read more.
Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting μ-uncertainties are described by the effective number theory whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive μ-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the μ-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum μ-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement. Full article
Article
Bose–Einstein Condensation Processes with Nontrivial Geometric Multiplicities Realized via 𝒫𝒯−Symmetric and Exactly Solvable Linear-Bose–Hubbard Building Blocks
Quantum Rep. 2021, 3(3), 517-533; https://doi.org/10.3390/quantum3030034 - 08 Sep 2021
Viewed by 248
Abstract
It is well known that, using the conventional non-Hermitian but PTsymmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase [...] Read more.
It is well known that, using the conventional non-Hermitian but PTsymmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity K = 1. In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose–Hubbard model, which remains exactly solvable while admitting any value of K1. It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose–Hubbard model. Full article
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Article
Theory of Photon Subtraction for Two-Mode Entangled Light Beams
Quantum Rep. 2021, 3(3), 500-516; https://doi.org/10.3390/quantum3030033 - 03 Sep 2021
Viewed by 260
Abstract
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions [...] Read more.
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation. Full article
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Article
Support Vector Machines with Quantum State Discrimination
Quantum Rep. 2021, 3(3), 482-499; https://doi.org/10.3390/quantum3030032 - 28 Aug 2021
Viewed by 446
Abstract
We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. [...] Read more.
We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification. Full article
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Article
On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution
Quantum Rep. 2021, 3(3), 473-481; https://doi.org/10.3390/quantum3030031 - 24 Aug 2021
Viewed by 277
Abstract
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced [...] Read more.
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator. Full article
Article
Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures
Quantum Rep. 2021, 3(3), 458-472; https://doi.org/10.3390/quantum3030030 - 21 Aug 2021
Cited by 1 | Viewed by 373
Abstract
We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete [...] Read more.
We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola–Kanai model as a particular case. Explicit solutions are given in both the classical and quantum pictures. Full article
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Article
Minimum Time for the Evolution to a Nonorthogonal Quantum State and Upper Bound of the Geometric Efficiency of Quantum Evolutions
Quantum Rep. 2021, 3(3), 444-457; https://doi.org/10.3390/quantum3030029 - 16 Aug 2021
Viewed by 389
Abstract
We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states A and B equals TAB=cos1A|B/ΔE with ΔE [...] Read more.
We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states A and B equals TAB=cos1A|B/ΔE with ΔE being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure ε of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality ε1 even when the system only passes through nonorthogonal quantum states. Full article
Article
A Transformation-Based Quantum Physical Synthesis Approach for Nearest-Neighbor Architectures
Quantum Rep. 2021, 3(3), 435-443; https://doi.org/10.3390/quantum3030028 - 15 Aug 2021
Viewed by 516
Abstract
The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run [...] Read more.
The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run a circuit on a nearest-neighbor architecture. Minimizing the number of SWAP operations potentially decreases the latency and error probability of a quantum circuit. Focusing on this concept, we present a physical synthesis technique based on transformation rules to decrease the number of SWAP operations in nearest-neighbor architectures. After the qubits of a circuit are mapped onto the physical qubits provided by the target architecture, our procedure is fed by this mapping information. Our method uses the obtained placement and scheduling information to apply some transformation rules to the original netlist to decrease the number of extra SWAP gates required for running the circuit on the architecture. We follow two policies in applying a transformation rule, greedy and simulated-annealing-based policies. Simulation results show that the proposed technique decreases the average number of extra SWAP operations by about 20.6% and 24.1% based on greedy and simulated-annealing-based policies, respectively, compared with the best in the literature. Full article
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Article
Mechanism of Proton Pumping in Complex I of the Mitochondrial Respiratory Chain
Quantum Rep. 2021, 3(3), 425-434; https://doi.org/10.3390/quantum3030027 - 09 Aug 2021
Viewed by 412
Abstract
We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other [...] Read more.
We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other end away from the proton site, thereby reducing its energy and allowing a proton to populate the site. When the electron escapes, elastic forces assist the return of the piston, increasing proton site energy and facilitating proton transfer. We derive the Heisenberg equations of motion for electron and proton operators and rewrite them in the form of rate equations coupled to the phenomenological Langevin equation describing piston dynamics. This set of coupled equations is solved numerically. We show that proton pumping can be achieved within this model for a reasonable set of parameters. The dependencies of proton current on geometry, temperature, and other parameters are examined. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Biology)
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Article
On Bell’s Inequality in PT-Symmetric Quantum Systems
Quantum Rep. 2021, 3(3), 417-424; https://doi.org/10.3390/quantum3030026 - 31 Jul 2021
Viewed by 712
Abstract
Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound [...] Read more.
Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved. Full article
Review
Generalized Probabilities in Statistical Theories
Quantum Rep. 2021, 3(3), 389-416; https://doi.org/10.3390/quantum3030025 - 29 Jul 2021
Viewed by 724
Abstract
We discuss different formal frameworks for the description of generalized probabilities in statistical theories. We analyze the particular cases of probabilities appearing in classical and quantum mechanics and the approach to generalized probabilities based on convex sets. We argue for considering quantum probabilities [...] Read more.
We discuss different formal frameworks for the description of generalized probabilities in statistical theories. We analyze the particular cases of probabilities appearing in classical and quantum mechanics and the approach to generalized probabilities based on convex sets. We argue for considering quantum probabilities as the natural probabilistic assignments for rational agents dealing with contextual probabilistic models. In this way, the formal structure of quantum probabilities as a non-Boolean probabilistic calculus is endowed with a natural interpretation. Full article
Article
The Underlying Order Induced by Orthogonality and the Quantum Speed Limit
Quantum Rep. 2021, 3(3), 376-388; https://doi.org/10.3390/quantum3030024 - 24 Jul 2021
Viewed by 499
Abstract
We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The [...] Read more.
We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality. Full article
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Article
A DFT Study on the Interaction of Doped Carbon Nanotubes with H2S, SO2 and Thiophene
Quantum Rep. 2021, 3(3), 366-375; https://doi.org/10.3390/quantum3030023 - 05 Jul 2021
Viewed by 554
Abstract
The interactions of simple and Al-, B-, N-, S-, P-, and Si-doped carbon nanotubes with three sulfur-containing molecules (H2S, SO2, and thiophene) were investigated to assess their adsorption potencies and sensor abilities. The DFT method was used to calculate [...] Read more.
The interactions of simple and Al-, B-, N-, S-, P-, and Si-doped carbon nanotubes with three sulfur-containing molecules (H2S, SO2, and thiophene) were investigated to assess their adsorption potencies and sensor abilities. The DFT method was used to calculate the adsorption energies and natural bond orbitals parameters. In addition, population analyses were performed to calculate the energy gaps and reactivity parameters. The results showed an exothermic interaction of H2S, SO2, and thiophene with simple and doped carbon nanotubes, while the maximum negative adsorption energies belong to Al- and B-containing complexes. Furthermore, evaluation of second-order perturbation energies (obtained from natural bond orbitals calculations) confirmed that the highest energies were related to B- and Al-containing intramolecular interactions. The results revealed the favorability of adsorption of SO2 by nanotubes (B- and Al-doped carbon nanotubes, in particular) compared with the other examined adsorbates. Full article
(This article belongs to the Special Issue Fundamentals and Applications in Quantum Chemistry)
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Article
Non-Gaussianity of Four-Photon Superpositions of Fock States
Quantum Rep. 2021, 3(3), 350-365; https://doi.org/10.3390/quantum3030022 - 01 Jul 2021
Viewed by 679
Abstract
We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the [...] Read more.
We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Optics 2021)
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