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Special Issue "Quantum Information and Foundations"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (28 February 2018)

Special Issue Editors

Guest Editor
Prof. Dr. Giacomo Mauro D'Ariano

QUit Group, Department of Physics, University of Pavia, I-27100 Pavia, Italy
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Phone: +39 0382 987 484
Fax: +39 0382 987 793
Interests: quantum information; foundations of quantum physics; foundations of quantum field theory; tension between quantum theory and general relativity
Guest Editor
Dr. Paolo Perinotti

QUit Group, Department of Physics, University of Pavia, Pavia, Italy
E-Mail
Interests: quantum foundations; quantum information theory; quantum cellular automata and quantum walks; foundations of quantum field theory; tension between quantum theory and general relativity

Special Issue Information

Dear Colleagues,

Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. On the fundamental side, the new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based for example on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton which has revealed new routes for exploring quantum fields theory both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations on the practical side. In this golden age of foundations, an astonishing number of new ideas, frameworks and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.

Prof. Giacomo Mauro D'Ariano
Dr. Paolo Perinotti
Guest Editors

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Keywords

  • Quantum information
  • quantum foundations
  • probabilistic theories
  • quantum computation
  • quantum communications
  • quantum field theory
  • quantum cellular automata
  • quantum walks
  • quantum simulations

Published Papers (24 papers)

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Open AccessArticle Solutions of a Two-Particle Interacting Quantum Walk
Entropy 2018, 20(6), 435; https://doi.org/10.3390/e20060435
Received: 22 April 2018 / Revised: 21 May 2018 / Accepted: 31 May 2018 / Published: 5 June 2018
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Abstract
We study the solutions of an interacting Fermionic cellular automaton which is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particle solutions of the automaton recently in the literature, which exploits the symmetries
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We study the solutions of an interacting Fermionic cellular automaton which is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particle solutions of the automaton recently in the literature, which exploits the symmetries of the evolution operator. In the two-particle sector, the evolution operator is given by the sequence of two steps, the first one corresponding to a unitary interaction activated by two-particle excitation at the same site, and the second one to two independent one-dimensional Dirac quantum walks. The interaction step can be regarded as the discrete-time version of the interacting term of some Hamiltonian integrable system, such as the Hubbard or the Thirring model. The present automaton exhibits scattering solutions with nontrivial momentum transfer, jumping between different regions of the Brillouin zone that can be interpreted as Fermion-doubled particles, in stark contrast with the customary momentum-exchange of the one-dimensional Hamiltonian systems. A further difference compared to the Hamiltonian model is that there exist bound states for every value of the total momentum and of the coupling constant. Even in the special case of vanishing coupling, the walk manifests bound states, for finitely many isolated values of the total momentum. As a complement to the analytical derivations we show numerical simulations of the interacting evolution. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Agents, Subsystems, and the Conservation of Information
Entropy 2018, 20(5), 358; https://doi.org/10.3390/e20050358
Received: 12 March 2018 / Revised: 26 April 2018 / Accepted: 5 May 2018 / Published: 10 May 2018
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Abstract
Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different agents. Here, we propose a way
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Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different agents. Here, we propose a way to define subsystems in general physical theories, including theories beyond quantum and classical mechanics. Our construction associates every agent A with a subsystem S A , equipped with its set of states and its set of transformations. In quantum theory, this construction accommodates the notion of subsystems as factors of a tensor product, as well as the notion of subsystems associated with a subalgebra of operators. Classical systems can be interpreted as subsystems of quantum systems in different ways, by applying our construction to agents who have access to different sets of operations, including multiphase covariant channels and certain sets of free operations arising in the resource theory of quantum coherence. After illustrating the basic definitions, we restrict our attention to closed systems, that is, systems where all physical transformations act invertibly and where all states can be generated from a fixed initial state. For closed systems, we show that all the states of all subsystems admit a canonical purification. This result extends the purification principle to a broader setting, in which coherent superpositions can be interpreted as purifications of incoherent mixtures. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle A No-Go Theorem for Observer-Independent Facts
Entropy 2018, 20(5), 350; https://doi.org/10.3390/e20050350
Received: 5 April 2018 / Revised: 29 April 2018 / Accepted: 2 May 2018 / Published: 8 May 2018
Cited by 1 | PDF Full-text (449 KB) | HTML Full-text | XML Full-text
Abstract
In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner’s friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend can in principle
[...] Read more.
In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner’s friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend can in principle verify his/her respective state assignments by performing an appropriate measurement. As manifested through a click in a detector or a specific position of the pointer, the outcomes of these measurements can be regarded as reflecting directly observable “facts”. Reviewing arXiv:1507.05255, I will derive a no-go theorem for observer-independent facts, which would be common both for Wigner and the friend. I will then analyze this result in the context of a newly-derived theorem arXiv:1604.07422, where Frauchiger and Renner prove that “single-world interpretations of quantum theory cannot be self-consistent”. It is argued that “self-consistency” has the same implications as the assumption that observational statements of different observers can be compared in a single (and hence an observer-independent) theoretical framework. The latter, however, may not be possible, if the statements are to be understood as relational in the sense that their determinacy is relative to an observer. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Entropy 2018, 20(4), 266; https://doi.org/10.3390/e20040266
Received: 19 January 2018 / Revised: 16 March 2018 / Accepted: 6 April 2018 / Published: 11 April 2018
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Abstract
A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it.
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A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 N ( ρ A B ) < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 ) -mode Gaussian states and an estimate of N for ( n + m ) -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle A Royal Road to Quantum Theory (or Thereabouts)
Entropy 2018, 20(4), 227; https://doi.org/10.3390/e20040227
Received: 15 January 2018 / Revised: 14 March 2018 / Accepted: 19 March 2018 / Published: 26 March 2018
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Abstract
This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy
[...] Read more.
This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together and allows some (but not too much) room for more exotic alternatives. (This is a leisurely summary, based on recent lectures, of material from the papers arXiv:1206:2897 and arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon. Some further ideas are also explored, developing the connection between conjugate systems and the possibility of forming stable measurement records and making connections between this approach and the categorical approach to quantum theory.) Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Finding a Hadamard Matrix by Simulated Quantum Annealing
Entropy 2018, 20(2), 141; https://doi.org/10.3390/e20020141
Received: 2 January 2018 / Revised: 6 February 2018 / Accepted: 16 February 2018 / Published: 22 February 2018
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Abstract
Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which
[...] Read more.
Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Robust Macroscopic Quantum Measurements in the Presence of Limited Control and Knowledge
Entropy 2018, 20(1), 39; https://doi.org/10.3390/e20010039
Received: 31 October 2017 / Revised: 8 December 2017 / Accepted: 26 December 2017 / Published: 9 January 2018
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Abstract
Quantum measurements have intrinsic properties that seem incompatible with our everyday-life macroscopic measurements. Macroscopic Quantum Measurement (MQM) is a concept that aims at bridging the gap between well-understood microscopic quantum measurements and macroscopic classical measurements. In this paper, we focus on the task
[...] Read more.
Quantum measurements have intrinsic properties that seem incompatible with our everyday-life macroscopic measurements. Macroscopic Quantum Measurement (MQM) is a concept that aims at bridging the gap between well-understood microscopic quantum measurements and macroscopic classical measurements. In this paper, we focus on the task of the polarization direction estimation of a system of N spins 1/2 particles and investigate the model some of us proposed in Barnea et al., 2017. This model is based on a von Neumann pointer measurement, where each spin component of the system is coupled to one of the three spatial component directions of a pointer. It shows traits of a classical measurement for an intermediate coupling strength. We investigate relaxations of the assumptions on the initial knowledge about the state and on the control over the MQM. We show that the model is robust with regard to these relaxations. It performs well for thermal states and a lack of knowledge about the size of the system. Furthermore, a lack of control on the MQM can be compensated by repeated “ultra-weak” measurements. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Entropic Updating of Probabilities and Density Matrices
Entropy 2017, 19(12), 664; https://doi.org/10.3390/e19120664
Received: 2 November 2017 / Revised: 1 December 2017 / Accepted: 2 December 2017 / Published: 4 December 2017
Cited by 2 | PDF Full-text (801 KB) | HTML Full-text | XML Full-text
Abstract
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel.
[...] Read more.
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle Quantum Information: What Is It All About?
Entropy 2017, 19(12), 645; https://doi.org/10.3390/e19120645
Received: 23 October 2017 / Revised: 16 November 2017 / Accepted: 22 November 2017 / Published: 29 November 2017
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Abstract
This paper answers Bell’s question: What does quantum information refer to? It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity
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This paper answers Bell’s question: What does quantum information refer to? It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity (PDI or framework) as a quantum sample space. The single framework rule of consistent histories prevents paradoxes or contradictions. When only one framework is employed, classical (Shannon) information theory can be imported unchanged into the quantum domain. A particular case is the macroscopic world of classical physics whose quantum description needs only a single quasiclassical framework. Nontrivial issues unique to quantum information, those with no classical analog, arise when aspects of two or more incompatible frameworks are compared. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle Structure of Multipartite Entanglement in Random Cluster-Like Photonic Systems
Entropy 2017, 19(9), 473; https://doi.org/10.3390/e19090473
Received: 24 July 2017 / Revised: 15 August 2017 / Accepted: 2 September 2017 / Published: 5 September 2017
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Abstract
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how quantum networking, embodied by the generation of a special class of
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Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how quantum networking, embodied by the generation of a special class of multipartite states called cluster states, can be used to achieve a powerful paradigm for quantum information processing. Here we analyze randomly generated cluster states in order to address the emergence of correlations as a function of the density of edges in a given underlying graph. We find that the most widespread multipartite entanglement does not correspond to the highest amount of edges in the cluster. We extend the analysis to higher dimensions, finding similar results, which suggest the establishment of small world structures in the entanglement sharing of randomised cluster states, which can be exploited in engineering more efficient quantum information carriers. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Planck-Scale Soccer-Ball Problem: A Case of Mistaken Identity
Entropy 2017, 19(8), 400; https://doi.org/10.3390/e19080400
Received: 23 April 2017 / Revised: 10 July 2017 / Accepted: 18 July 2017 / Published: 2 August 2017
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Abstract
Over the last decade, it has been found that nonlinear laws of composition of momenta are predicted by some alternative approaches to “real” 4D quantum gravity, and by all formulations of dimensionally-reduced (3D) quantum gravity coupled to matter. The possible relevance for rather
[...] Read more.
Over the last decade, it has been found that nonlinear laws of composition of momenta are predicted by some alternative approaches to “real” 4D quantum gravity, and by all formulations of dimensionally-reduced (3D) quantum gravity coupled to matter. The possible relevance for rather different quantum-gravity models has motivated several studies, but this interest is being tempered by concerns that a nonlinear law of addition of momenta might inevitably produce a pathological description of the total momentum of a macroscopic body. I here show that such concerns are unjustified, finding that they are rooted in failure to appreciate the differences between two roles for laws composition of momentum in physics. Previous results relied exclusively on the role of a law of momentum composition in the description of spacetime locality. However, the notion of total momentum of a multi-particle system is not a manifestation of locality, but rather reflects translational invariance. By working within an illustrative example of quantum spacetime, I show explicitly that spacetime locality is indeed reflected in a nonlinear law of composition of momenta, but translational invariance still results in an undeformed linear law of addition of momenta building up the total momentum of a multi-particle system. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle Quantum Genetic Learning Control of Quantum Ensembles with Hamiltonian Uncertainties
Entropy 2017, 19(8), 376; https://doi.org/10.3390/e19080376
Received: 9 April 2017 / Revised: 5 July 2017 / Accepted: 19 July 2017 / Published: 1 August 2017
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Abstract
In this paper, a new method for controlling a quantum ensemble that its members have uncertainties in Hamiltonian parameters is designed. Based on combining the sampling-based learning control (SLC) and a new quantum genetic algorithm (QGA) method, the control of an ensemble of
[...] Read more.
In this paper, a new method for controlling a quantum ensemble that its members have uncertainties in Hamiltonian parameters is designed. Based on combining the sampling-based learning control (SLC) and a new quantum genetic algorithm (QGA) method, the control of an ensemble of a two-level quantum system with Hamiltonian uncertainties is achieved. To simultaneously transfer the ensemble members to a desired state, an SLC algorithm is designed. For reducing the transfer error significantly, an optimization problem is defined. Considering the advantages of QGA and the nature of the problem, the optimization problem by using the QGA method is solved. For this purpose, N samples through sampling of the uncertainty parameters via uniform distribution are generated and an augmented system is also created. By using QGA in the training step, the best control signal is obtained. To test the performance and validation of the method, the obtained control is implemented for some random selected samples. A couple of examples are simulated for investigating the proposed model. The results of the simulations indicate the effectiveness and the advantages of the proposed method. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Discrete Wigner Function Derivation of the Aaronson–Gottesman Tableau Algorithm
Entropy 2017, 19(7), 353; https://doi.org/10.3390/e19070353
Received: 3 May 2017 / Revised: 28 June 2017 / Accepted: 4 July 2017 / Published: 11 July 2017
Cited by 2 | PDF Full-text (324 KB) | HTML Full-text | XML Full-text
Abstract
The Gottesman–Knill theorem established that stabilizer states and Clifford operations can be efficiently simulated classically. For qudits with odd dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a
[...] Read more.
The Gottesman–Knill theorem established that stabilizer states and Clifford operations can be efficiently simulated classically. For qudits with odd dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a discrete Wigner function-based simulation algorithm for odd-d qudits that has the same time and space complexity as the Aaronson–Gottesman algorithm for qubits. We show that the efficiency of both algorithms is due to harmonic evolution in the symplectic structure of discrete phase space. The differences between the Wigner function algorithm for odd-d and the Aaronson–Gottesman algorithm for qubits are likely due only to the fact that the Weyl–Heisenberg group is not in S U ( d ) for d = 2 and that qubits exhibit state-independent contextuality. This may provide a guide for extending the discrete Wigner function approach to qubits. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Iterant Algebra
Entropy 2017, 19(7), 347; https://doi.org/10.3390/e19070347
Received: 29 May 2017 / Revised: 26 June 2017 / Accepted: 5 July 2017 / Published: 11 July 2017
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Abstract
We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view
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We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Concepts and Criteria for Blind Quantum Source Separation and Blind Quantum Process Tomography
Entropy 2017, 19(7), 311; https://doi.org/10.3390/e19070311
Received: 6 April 2017 / Revised: 9 June 2017 / Accepted: 23 June 2017 / Published: 6 July 2017
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Abstract
Blind Source Separation (BSS) is an active domain of Classical Information Processing, with well-identified methods and applications. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS), with a recent extension towards Blind Quantum Process Tomography
[...] Read more.
Blind Source Separation (BSS) is an active domain of Classical Information Processing, with well-identified methods and applications. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS), with a recent extension towards Blind Quantum Process Tomography (BQPT). This article investigates the use of several fundamental quantum concepts in the BQSS context and establishes properties already used without justification in that context. It mainly considers a pair of electron spins initially separately prepared in a pure state and then submitted to an undesired exchange coupling between these spins. Some consequences of the existence of the entanglement phenomenon, and of the probabilistic aspect of quantum measurements, upon BQSS solutions, are discussed. An unentanglement criterion is established for the state of an arbitrary qubit pair, expressed first with probability amplitudes and secondly with probabilities. The interest of using the concept of a random quantum state in the BQSS context is presented. It is stressed that the concept of statistical independence of the sources, widely used in classical BSS, should be used with care in BQSS, and possibly replaced by some disentanglement principle. It is shown that the coefficients of the development of any qubit pair pure state over the states of an orthonormal basis can be expressed with the probabilities of results in the measurements of well-chosen spin components. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Non-Causal Computation
Entropy 2017, 19(7), 326; https://doi.org/10.3390/e19070326
Received: 11 May 2017 / Revised: 22 June 2017 / Accepted: 30 June 2017 / Published: 2 July 2017
Cited by 7 | PDF Full-text (307 KB) | HTML Full-text | XML Full-text
Abstract
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a novel computing paradigm beyond
[...] Read more.
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a novel computing paradigm beyond quantum computing, replacing this assumption by mere logical consistency: We study non-causal circuits, where a fixed time structure within a gate is locally assumed whilst the global causal structure between the gates is dropped. We present examples of logically consistent non-causal circuits outperforming all causal ones; they imply that suppressing loops entirely is more restrictive than just avoiding the contradictions they can give rise to. That fact is already known for correlations as well as for communication, and we here extend it to computation. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Entropic Phase Maps in Discrete Quantum Gravity
Entropy 2017, 19(7), 322; https://doi.org/10.3390/e19070322
Received: 26 May 2017 / Revised: 20 June 2017 / Accepted: 25 June 2017 / Published: 30 June 2017
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Abstract
Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar
[...] Read more.
Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle CSL Collapse Model Mapped with the Spontaneous Radiation
Entropy 2017, 19(7), 319; https://doi.org/10.3390/e19070319
Received: 30 April 2017 / Revised: 13 June 2017 / Accepted: 25 June 2017 / Published: 29 June 2017
Cited by 7 | PDF Full-text (278 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission
[...] Read more.
In this paper, new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows the obtainment of the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate λ and the correlation length r C are mapped, thus allowing the exclusion of a broad range of the parameter space. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessArticle Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation
Entropy 2017, 19(7), 301; https://doi.org/10.3390/e19070301
Received: 26 May 2017 / Revised: 21 June 2017 / Accepted: 21 June 2017 / Published: 24 June 2017
Cited by 4 | PDF Full-text (436 KB) | HTML Full-text | XML Full-text
Abstract
Heisenberg’s uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in various ways. The relative entropy is the natural theoretical quantifier
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Heisenberg’s uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in various ways. The relative entropy is the natural theoretical quantifier of the information loss when a `true’ probability distribution is replaced by an approximating one. In this paper, we provide a lower bound for the amount of information that is lost by replacing the distributions of the sharp position and momentum observables, as they could be obtained with two separate experiments, by the marginals of any smeared joint measurement. The bound is obtained by introducing an entropic error function, and optimizing it over a suitable class of covariant approximate joint measurements. We fully exploit two cases of target observables: (1) n-dimensional position and momentum vectors; (2) two components of position and momentum along different directions. In (1), we connect the quantum bound to the dimension n; in (2), going from parallel to orthogonal directions, we show the transition from highly incompatible observables to compatible ones. For simplicity, we develop the theory only for Gaussian states and measurements. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle Ruling out Higher-Order Interference from Purity Principles
Entropy 2017, 19(6), 253; https://doi.org/10.3390/e19060253
Received: 21 April 2017 / Revised: 21 May 2017 / Accepted: 22 May 2017 / Published: 1 June 2017
Cited by 5 | PDF Full-text (383 KB) | HTML Full-text | XML Full-text
Abstract
As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits; there are no genuinely new features resulting from considering three
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As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits; there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the interference pattern has an irreducible dependence. Many authors have wondered why quantum interference is limited to the second level of this hierarchy. Does the existence of higher-order interference violate some natural physical principle that we believe should be fundamental? In the current work we show that such principles can be found which limit interference behaviour to second-order, or “quantum-like”, interference, but that do not restrict us to the entire quantum formalism. We work within the operational framework of generalised probabilistic theories, and prove that any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification—four principles that formalise the fundamental character of purity in nature—exhibits at most second-order interference. Hence these theories are, at least conceptually, very “close” to quantum theory. Along the way we show that systems in such theories correspond to Euclidean Jordan algebras. Hence, they are self-dual and, moreover, multi-slit experiments in such theories are described by pure projectors. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle Leaks: Quantum, Classical, Intermediate and More
Entropy 2017, 19(4), 174; https://doi.org/10.3390/e19040174
Received: 26 January 2017 / Revised: 30 March 2017 / Accepted: 12 April 2017 / Published: 19 April 2017
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Abstract
We introduce the notion of a leak for general process theories and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence
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We introduce the notion of a leak for general process theories and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence leaks to quantum theory. Finally, we show that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory, a feature missing in standard definitions; hence, we propose a refined definition and study the resulting notion of purity for quantum, classical and intermediate theories. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
Open AccessArticle The Many Classical Faces of Quantum Structures
Entropy 2017, 19(4), 144; https://doi.org/10.3390/e19040144
Received: 9 January 2017 / Revised: 22 February 2017 / Accepted: 23 March 2017 / Published: 29 March 2017
Cited by 1 | PDF Full-text (323 KB) | HTML Full-text | XML Full-text
Abstract
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)

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Open AccessReview Quantum Theory from Rules on Information Acquisition
Entropy 2017, 19(3), 98; https://doi.org/10.3390/e19030098
Received: 23 January 2017 / Accepted: 17 February 2017 / Published: 3 March 2017
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Abstract
We summarize a recent reconstruction of the quantum theory of qubits from rules constraining an observer’s acquisition of information about physical systems. This review is accessible and fairly self-contained, focusing on the main ideas and results and not the technical details. The reconstruction
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We summarize a recent reconstruction of the quantum theory of qubits from rules constraining an observer’s acquisition of information about physical systems. This review is accessible and fairly self-contained, focusing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and specifically for its correlation structure. In particular, it explains entanglement, monogamy and non-locality compellingly from limited accessible information and complementarity. As a by-product, it also unravels new ‘conserved informational charges’ from complementarity relations that characterize the unitary group and the set of pure states. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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Open AccessBrief Report Test of the Pauli Exclusion Principle in the VIP-2 Underground Experiment
Entropy 2017, 19(7), 300; https://doi.org/10.3390/e19070300
Received: 29 April 2017 / Revised: 6 June 2017 / Accepted: 22 June 2017 / Published: 24 June 2017
Cited by 5 | PDF Full-text (1292 KB) | HTML Full-text | XML Full-text
Abstract
The validity of the Pauli exclusion principle—a building block of Quantum Mechanics—is tested for electrons. The VIP (violation of Pauli exclusion principle) and its follow-up VIP-2 experiments at the Laboratori Nazionali del Gran Sasso search for X-rays from copper atomic transitions that are
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The validity of the Pauli exclusion principle—a building block of Quantum Mechanics—is tested for electrons. The VIP (violation of Pauli exclusion principle) and its follow-up VIP-2 experiments at the Laboratori Nazionali del Gran Sasso search for X-rays from copper atomic transitions that are prohibited by the Pauli exclusion principle. The candidate events—if they exist—originate from the transition of a 2 p orbit electron to the ground state which is already occupied by two electrons. The present limit on the probability for Pauli exclusion principle violation for electrons set by the VIP experiment is 4.7 × 10 29 . We report a first result from the VIP-2 experiment improving on the VIP limit, which solidifies the final goal of achieving a two orders of magnitude gain in the long run. Full article
(This article belongs to the Special Issue Quantum Information and Foundations)
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