Special Issue "Selected Papers from the 16th International Conference on Squeezed States and Uncertainty Relations (ICSSUR 2019)"

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 16959

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Special Issue Editors

Prof. Dr. Margarita A. Man’ko
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Guest Editor
Lebedev Physical Institute, Leninskii Prospect 53, 119991 Moscow, Russia
Interests: interpretations of quantum mechanics; the probabilistic structure of Bell’s inequality; quantum and classical probability; entanglement and Bell-type inequalities; quantum optics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luis L. Sánchez-Soto
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Guest Editor
Faculty of Physics, Complutense University of Madrid, Ciudad Universitaria, 28040 Madrid, Spain
Interests: quantum optics; quantum information; polarization; tomography; discrete quantum systems; phase-space method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will publish selected papers from the 16th International Conference on Squeezed States and Uncertainty Relations (ICSSUR 2019), which will take place on 17–21 June 2019 in Madrid, Spain. Submissions should be received before the start of the conference and will be rapidly reviewed during or shortly after the conference.

ICSSUR covers a wide range of topics from quantum optics to quantum atom optics and quantum information:

  • coherent states and squeezed states;
  • uncertainty relations;
  • quantum superpositions;
  • entanglement and decoherence;
  • phase-space methods; implementations of quantum computation and communication;
  • continuous variables and quantum-information processing with continuous variables;
  • twin photons, including their sources, properties, and applications;
  • photon-number-resolving detectors, homodyne detection, and other detection techniques;
  • atom and molecular optics with emphasis on non-classical behavior;
  • cavity and circuit QED;
  • quantum memories and quantum gates;
  • quantum propagation;
  • quantum key distribution.

In addition to the above, related topics are included.

Over the years, ICSSUR), initiated by Professor Young Suh Kim, evolved from a meeting on optical quantum measurement to one covering a much wider range of topics. The locations of the previous fourteen conferences were as follows:

Prof. Dr. Margarita A. Man’ko
Prof. Dr. Luis L Sánchez-Soto
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (14 papers)

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Editorial

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Editorial
Editorial for the Special Issue “Selected Papers from the 16th International Conference on Squeezed States and Uncertainty Relations (ICSSUR 2019)”
Quantum Rep. 2020, 2(3), 450-452; https://doi.org/10.3390/quantum2030031 - 02 Sep 2020
Viewed by 966
Abstract
The first quantum revolution started in the early 20th century and gave us new rules that govern physical reality [...] Full article

Research

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Article
Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions
Quantum Rep. 2020, 2(1), 64-79; https://doi.org/10.3390/quantum2010006 - 21 Jan 2020
Cited by 2 | Viewed by 891
Abstract
The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the [...] Read more.
The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the probability distributions which determine quantum states with the Feynman path integral is found. The time-dependent phase of the wave function is related to the time-dependent probability distribution which determines the density matrix. The formal classical-like random variables associated with quantum observables for qubit systems are considered, and the connection of the statistics of the quantum observables with the classical statistics of the random variables is discussed. Full article
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Article
Distance between Bound Entangled States from Unextendible Product Bases and Separable States
Quantum Rep. 2020, 2(1), 49-56; https://doi.org/10.3390/quantum2010004 - 13 Jan 2020
Cited by 7 | Viewed by 979
Abstract
We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between [...] Read more.
We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between the reference state, entanglement of which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds an approximation of CSS. In this article, we investigate if this approximation can be good enough to yield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those given by Bandyopadhyay–Ghosh–Roychowdhury (BGR) construction. This comparison allows us to learn about the amount of entanglement and we find a relationship between it and a feature of the construction of UPBBE states, namely the size of their central tile. We show that in most studied cases, witnesses found with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay, Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections in a realization of the state. Full article
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Article
Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum
Quantum Rep. 2020, 2(1), 12-38; https://doi.org/10.3390/quantum2010002 - 27 Dec 2019
Cited by 9 | Viewed by 1194
Abstract
In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the [...] Read more.
In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non- P T -symmetric and P T -symmetric oscillators exhibiting real spectra. Full article
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Article
Remembering George Sudarshan
Quantum Rep. 2019, 1(2), 271-276; https://doi.org/10.3390/quantum1020024 - 02 Dec 2019
Cited by 1 | Viewed by 849
Abstract
In these brief notes we want to render homage to the memory of E.C.G. Sudarshan, adding it to the many contributions devoted to preserve his memory from a personal point of view. Full article
Article
Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators
Quantum Rep. 2019, 1(2), 260-270; https://doi.org/10.3390/quantum1020023 - 15 Nov 2019
Cited by 6 | Viewed by 1235
Abstract
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the [...] Read more.
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the S U ( 2 ) coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space. Full article
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Article
Einstein’s E = mc2 Derivable from Heisenberg’s Uncertainty Relations
Quantum Rep. 2019, 1(2), 236-251; https://doi.org/10.3390/quantum1020021 - 09 Nov 2019
Cited by 2 | Viewed by 2181
Abstract
Heisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the Sp(2) group which is isomorphic to [...] Read more.
Heisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the O ( 2 , 1 ) group. This group has three independent generators. The one-dimensional step-up and step-down operators can be combined into one two-by-two Hermitian matrix which contains three independent operators. If we use a two-variable Heisenberg commutation relation, the two pairs of independent step-up, step-down operators can be combined into a four-by-four block-diagonal Hermitian matrix with six independent parameters. It is then possible to add one off-diagonal two-by-two matrix and its Hermitian conjugate to complete the four-by-four Hermitian matrix. This off-diagonal matrix has four independent generators. There are thus ten independent generators. It is then shown that these ten generators can be linearly combined to the ten generators for Dirac’s two oscillator system leading to the group isomorphic to the de Sitter group O ( 3 , 2 ) , which can then be contracted to the inhomogeneous Lorentz group with four translation generators corresponding to the four-momentum in the Lorentz-covariant world. This Lorentz-covariant four-momentum is known as Einstein’s E = m c 2 . Full article
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Article
Mutually Unbiased Bases and Their Symmetries
Quantum Rep. 2019, 1(2), 226-235; https://doi.org/10.3390/quantum1020020 - 08 Nov 2019
Cited by 1 | Viewed by 897
Abstract
We present and generalize the basic ideas underlying recent work aimed at the construction of mutually unbiased bases in finite dimensional Hilbert spaces with the help of group and graph theoretical concepts. In this approach finite groups are used to construct maximal sets [...] Read more.
We present and generalize the basic ideas underlying recent work aimed at the construction of mutually unbiased bases in finite dimensional Hilbert spaces with the help of group and graph theoretical concepts. In this approach finite groups are used to construct maximal sets of mutually unbiased bases. Thus the prime number restrictions of previous approaches are circumvented and this construction principle sheds new light onto the intricate relation between mutually unbiased bases and characteristic geometrical structures of Hilbert spaces. Full article
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Article
A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids
Quantum Rep. 2019, 1(2), 193-207; https://doi.org/10.3390/quantum1020017 - 28 Oct 2019
Cited by 6 | Viewed by 1076
Abstract
We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form [...] Read more.
We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) y ( 1 + β ) , x ( 1 β ) / 2 . Such potentials with β 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields. Full article
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Article
Descriptions of Relativistic Dynamics with World Line Condition
Quantum Rep. 2019, 1(2), 181-192; https://doi.org/10.3390/quantum1020016 - 19 Oct 2019
Cited by 2 | Viewed by 968
Abstract
In this paper, a generalized form of relativistic dynamics is presented. A realization of the Poincaré algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in R4. The construction of this realization is explicitly [...] Read more.
In this paper, a generalized form of relativistic dynamics is presented. A realization of the Poincaré algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in R 4 . The construction of this realization is explicitly shown to clarify the role of the commutation relations of the Poincaré algebra versus their description in terms of Poisson brackets in the no-interaction theorem. Moreover, a geometrical analysis of the “eleventh generator” formalism introduced by Sudarshan and Mukunda is outlined, this formalism being at the basis of many proposals which evaded the no-interaction theorem. Full article
Article
On the Prospects of Multiport Devices for Photon-Number-Resolving Detection
Quantum Rep. 2019, 1(2), 162-180; https://doi.org/10.3390/quantum1020015 - 29 Sep 2019
Cited by 2 | Viewed by 1401
Abstract
Ideal photon-number-resolving detectors form a class of important optical components in quantum optics and quantum information theory. In this article, we theoretically investigate the potential of multiport devices having reconstruction performances approaching that of the Fock-state measurement. By recognizing that all multiport devices [...] Read more.
Ideal photon-number-resolving detectors form a class of important optical components in quantum optics and quantum information theory. In this article, we theoretically investigate the potential of multiport devices having reconstruction performances approaching that of the Fock-state measurement. By recognizing that all multiport devices are minimally complete, we first provide a general analytical framework to describe the tomographic accuracy (or quality) of these devices. Next, we show that a perfect multiport device with an infinite number of output ports functions as either the Fock-state measurement when photon losses are absent or binomial mixtures of Fock-state measurements when photon losses are present and derive their respective expressions for the tomographic transfer function. This function is the scaled asymptotic mean squared error of the reconstructed photon-number distributions uniformly averaged over all distributions in the probability simplex. We then supply more general analytical formulas for the transfer function for finite numbers of output ports in both the absence and presence of photon losses. The effects of photon losses on the photon-number resolving power of both infinite- and finite-size multiport devices are also investigated. Full article
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Article
Superposition Principle and Born’s Rule in the Probability Representation of Quantum States
Quantum Rep. 2019, 1(2), 130-150; https://doi.org/10.3390/quantum1020013 - 26 Sep 2019
Cited by 10 | Viewed by 1349
Abstract
The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it [...] Read more.
The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states. Full article
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Article
Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup
Quantum Rep. 2019, 1(1), 63-70; https://doi.org/10.3390/quantum1010007 - 08 Jul 2019
Cited by 2 | Viewed by 1140
Abstract
We propose a dissipative scheme to prepare maximally entangled steady states in cavity QED setup, consisting of two two-level atoms interacting with the two counter-propagating whispering-gallery modes (WGMs) of a microtoroidal resonator. Using spontaneous emission and cavity decay as the dissipative quantum dynamical [...] Read more.
We propose a dissipative scheme to prepare maximally entangled steady states in cavity QED setup, consisting of two two-level atoms interacting with the two counter-propagating whispering-gallery modes (WGMs) of a microtoroidal resonator. Using spontaneous emission and cavity decay as the dissipative quantum dynamical source, we show that the steady state of this system can be steered into a two-atom single state as well as into a two-mode single state. We probed the compound system with weak field coupled to the system via a tapered fiber waveguide, finding it is possible to determine whether the two atoms or two modes are driven to a maximally entangled state. Through the transmission and reflection measurements, without disturbing the atomic state, when the cavity modes are being driven, or without disturbing the cavity field state, when a single atom being driven, one can get the information about the maximal entanglement. We also investigated for both subsystem, two-atom and two-mode states, the entanglement generation and under what conditions one can transfer entanglement from one subsystem to the other. Our scheme can be selectively used to prepare both maximally entangled atomic state as well as maximally entangled cavity-modes state, providing an efficient method for quantum information processing. Full article
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Review

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Review
Resource Theories of Nonclassical Light
Quantum Rep. 2019, 1(2), 151-161; https://doi.org/10.3390/quantum1020014 - 26 Sep 2019
Cited by 6 | Viewed by 1270
Abstract
In this focused review we survey recent progress in the development of resource theories of nonclassical light. We introduce the resource theoretical approach, in particular how it pertains to bosonic/light fields, and discuss several different formulations of resource theories of nonclassical light. Full article
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