Maximally entangled mixed states and conditional entropies

Batle, Josep Amengual i; Casas, M.; Plastino, A.

doi:10.1103/physreva.71.024301

Cited by 31 publications

(26 citation statements)

References 28 publications

(38 reference statements)

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“…One of the most fundamental concepts in the quantum description of nature is that of entanglement [1,2,3,4,5], which in recent years has been the subject of intense research efforts (see, for instance, the following, by no means exhaustive list of references: [1,2,3,4,5,6,7,8,9,10]). A state of a composite quantum system is called "entangled" if it cannot be represented as a mixture of factorizable pure states.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and the lower bounds on the speed of quantum evolution

2006

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The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state ψ I may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 67, 052109 (2003)] this bound has been generalized to the case where ψ I does not necessarily evolve into an orthogonal state, but into any other ψ F . It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with ψ F a not necessarily orthogonal state to ψ I . We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.

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Section: Introductionmentioning

confidence: 99%

Entanglement and the lower bounds on the speed of quantum evolution

2006

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“…In the limit q → 1 the Rényi entropy reduces to the von Neumann entropy. Note that the entropic criteria considered in [17][18][19][20][21][22][23] and in the present work, which depend on the entropies of the total and reduced density matrices, are different from those studied in [24], which involve entropic uncertainty relations associated with the measurement of particular observables.…”

Section: Introductionmentioning

confidence: 67%

“…Entropic separability criteria have played a distinguished role in the study of the entanglement-related features of mixed states of multipartite systems constituted by distinguishable subsystems [17][18][19][20][21][22][23]. For this kind of composite quantum systems, non-entangled states behave classically in the sense that the entropy of a subsystem is always less or equal than the entropy of the whole system.…”

Section: Introductionmentioning

confidence: 99%

Entropic entanglement criteria for Fermion systems

2012

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Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi's entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi's entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.

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“…Alternatively, one can consider the Rényi or the Tsallis families of q-entropies [25][26][27], respectively given by…”

Section: Characterization Of Entanglement Via the Variances Of Prmentioning

confidence: 99%

Uncertainty relations and entanglement in fermion systems

Zander

Plastino

2010

Phys. Rev. A

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The violation of uncertainty relations is used as a signature of entanglement for both pure and mixed states of two identical fermions. In the case of fermions with a four dimensional single particle Hilbert space we obtain several different types of uncertainty-related entanglement criteria based on local uncertainty relations, on the sum of variances of projectors, and on various entropic measures. Within the latter approach we consider either entropic uncertainty relations involving a single observable or relations based upon the sum of entropies associated with more than one observable. We extend the projector based entanglement criterion to the case of two-fermion and three-fermion systems with a six dimensional single particle Hilbert space.

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Maximally entangled mixed states and conditional entropies

Cited by 31 publications

References 28 publications

Entanglement and the lower bounds on the speed of quantum evolution

Entanglement and the lower bounds on the speed of quantum evolution

Entropic entanglement criteria for Fermion systems

Uncertainty relations and entanglement in fermion systems

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