GENERALIZED COMPLEMENTARITY RELATIONS IN COMPOSITE QUANTUM SYSTEMS OF ARBITRARY DIMENSIONS

Complementarity relations in composite bipartite quantum systems of arbitrary dimensions are proposed. Genuine bipartite quantum properties whose information content is quantified by the generalized concurrence mutually exclude the single-partite properties of the subsystems. The single-partite properties are determined by generalized predictabilities and visibilities, i.e. by the traditional concepts of wave-particle duality and define two complementary realities. These properties combined together are complementary to the generalized I-concurrence which quantifies genuine quantum correlations in n ⊗ m-dimensional bipartite systems. An important feature of the proposed quantitative complementarity relation is its upper bound which is given by a dimensional-dependent factor that exceeds unity in case of qudits with dimensionality d > 2. In d > 2-dimensional systems the information content can exceed one bit of information.

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Parametrizing Density Matrices for Composite Quantum Systems

Open Systems & Information Dynamics ◽

10.1142/s1230161208000274 ◽

2008 ◽

Vol 15 (04) ◽

pp. 397-408 ◽

Cited By ~ 4

Author(s):

Erwin Brüning ◽

Dariusz Chruściński ◽

Francesco Petruccione

Keyword(s):

Unitary Group ◽

Quantum Systems ◽

Density Matrices ◽

Density Operators ◽

Quantum Properties ◽

Bipartite Quantum Systems

A parametrization of density operators for bipartite quantum systems is proposed. It is based on the particular parametrization of the unitary group found recently by Jarlskog. It is expected that this parametrization will find interesting applications in the study of quantum properties of multipartite systems.

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Ergotropy from quantum and classical correlations

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac3eba ◽

2021 ◽

Author(s):

Akram Touil ◽

Baris Cakmak ◽

Sebastian Deffner

Keyword(s):

Quantum Correlations ◽

Quantum Systems ◽

Thermal Bath ◽

Quantum Properties ◽

Thermodynamic Work ◽

Qubit System ◽

Established Fact ◽

Quantum Mutual Information ◽

Quantum And Classical Correlations ◽

Thermal States

Abstract It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the ergotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.

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Cyclic quantum causal models

Nature Communications ◽

10.1038/s41467-020-20456-x ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Jonathan Barrett ◽

Robin Lorenz ◽

Ognyan Oreshkov

Keyword(s):

Causal Reasoning ◽

Causal Structure ◽

Bell Inequalities ◽

Quantum Correlations ◽

Quantum Systems ◽

Causal Models ◽

Causal Order ◽

Quantum Processes ◽

Causal Explanations ◽

Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

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A matrix realignment method for recognizing entanglement

Quantum Information and Computation ◽

10.26421/qic3.3-1 ◽

2003 ◽

Vol 3 (3) ◽

pp. 193-202

Author(s):

K. Chen ◽

L.-A. Wu

Keyword(s):

Kronecker Product ◽

Singular Values ◽

Quantum Systems ◽

Entangled States ◽

Approximation Technique ◽

Separable State ◽

Simple Method ◽

Bipartite Quantum Systems ◽

The Matrix ◽

Degree Of Entanglement

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

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Separability criteria based on the Bloch representation of density matrices

Quantum Information and Computation ◽

10.26421/qic7.7-5 ◽

2007 ◽

Vol 7 (7) ◽

pp. 624-638

Author(s):

J. de Vicente

Keyword(s):

Sufficient Conditions ◽

Quantum Systems ◽

Necessary Condition ◽

Sufficient Condition ◽

Pure Product ◽

Separability Problem ◽

Arbitrary Dimensions ◽

Necessary And Sufficient ◽

Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

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Quantized toroidal dipole eigenvalues in nano-systems

Journal of Physics Conference Series ◽

10.1088/1742-6596/2090/1/012151 ◽

2021 ◽

Vol 2090 (1) ◽

pp. 012151

Author(s):

D. V. Anghel ◽

A. T. Preda

Keyword(s):

Parity Violation ◽

Nuclear Reactions ◽

General Procedure ◽

Quantum Systems ◽

Electromagnetic Structure ◽

New Class ◽

Quantum Properties ◽

Commuting Operators ◽

Dipole Operator ◽

Theoretical Considerations

Abstract The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. This corresponds to the toroidal dipole operator T ^ in quantum systems, with the projections T ^ i (i = 1, 2, 3) on the coordinate axes. These operators are observables if they are self-adjoint, but, although it is commonly discussed of toroidal dipoles of both, classical and quantum systems, up to now no system has been identified in which the operators are self-adjoint. Therefore, in this paper we use what are called the “natural coordinates” of the T ^ 3 operator to give a general procedure to construct operators that commute with T ^ 3 . Using this method, we introduce the operators p ^ ( k ) , p ^ ( k 1 ) , and p ^ ( k 2 ) , which, together with T ^ 3 and L ^ 3 , form sets of commuting operators: ( p ^ ( k ) , T ^ 3 , L ^ 3 ) and ( p ^ ( k 1 ) , p ^ ( k 2 ) , T ^ 3 ) . All these theoretical considerations open up the possibility to design metamaterials that could exploit the quantization and the general quantum properties of the toroidal dipoles.

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Dynamics of Interacting Classical and Quantum Systems

Open Systems & Information Dynamics ◽

10.1142/s1230161211000236 ◽

2011 ◽

Vol 18 (04) ◽

pp. 339-351 ◽

Cited By ~ 7

Author(s):

Dariusz Chruściński ◽

Andrzej Kossakowski ◽

Giuseppe Marmo ◽

E. C. G. Sudarshan

Keyword(s):

Characteristic Feature ◽

Quantum Dynamics ◽

Quantum Discord ◽

Main Idea ◽

Quantum Correlations ◽

Quantum Systems ◽

Quantum States ◽

Algebra Of Observables ◽

Classical Quantum ◽

True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

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