Bipartite entanglement in systems of identical particles: The partial transposition criterion

Benatti, Fabio; Floreanini, Roberto; Marzolino, Ugo

doi:10.1016/j.aop.2012.02.002

Cited by 64 publications

(148 citation statements)

References 67 publications

Supporting

Mentioning

147

Contrasting

Order By: Relevance

“…But, as a closer look at the literature on the subject [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] reveals, it is apparent that there is no consensus yet as to what the proper formalism should be.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and Particle Identity: A Unifying Approach

et al. 2013

View full text Add to dashboard Cite

A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to a subalgebra. For bipartite systems of nonidentical particles, this approach reproduces the standard results. But it also very naturally overcomes the limitations of the usual treatment of systems of identical particles. This GNS approach seems very general and can be applied for example to systems obeying para-and braid-statistics including anyons.

show abstract

Section: Introductionmentioning

confidence: 99%

Entanglement and Particle Identity: A Unifying Approach

et al. 2013

View full text Add to dashboard Cite

show abstract

“…It is clearly shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the QPT, when the system is most chaotic. When a quantum many-body system undergoes a QPT, there is always a noticeable change in many ground state quantities, such as particle number statistics and the entanglement measure at the critical point [35][36][37]. However, it is not necessarily true that the system is most entangled at the critical point.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, a noticeable change in the ground state Shannon information entropy near or at the critical point can also be observed when j is large. Anyway, the above analysis justifies the connection of particle number statistics with entanglement observed in [35][36][37]. …”

Section: The Qpt and Entanglementmentioning

confidence: 99%

“…For instance, the variance of the particle number in a subgroup is an entanglement measure of the corresponding mode-bipartition for any pure state [35]. Moreover, coherence between subspaces of fixed particle number in a subgroup immediately implies mode entanglement [36,37]. It is clearly shown in this paper that, besides the ground state mean photon number and the ground state atomic inversion, as shown previously [10], the QPT in the Dicke model can also be observed in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.…”

Section: The Qpt and Entanglementmentioning

confidence: 99%

See 1 more Smart Citation

The Critical Point Entanglement and Chaos in the Dicke Model

Bao

Pan

et al. 2015

Entropy

View full text Add to dashboard Cite

Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.

show abstract

“…The characterization of quantum correlations with identical particles cannot rely on the tensor product structure of single particle Hilbert spaces, but must be reformulated in terms of subsets of locally manipulable observables [23,24,25,26,16,27,28]. This powerful approach generalizes the theory of entanglement of distinguishable particles.…”

mentioning

confidence: 99%

Entanglement in dissipative dynamics of identical particles

Marzolino¹

2013

EPL

Self Cite

View full text Add to dashboard Cite

Entanglement of identical massive particles recently gained attention, because of its relevance in highly controllable systems, e.g. ultracold gases. It accounts for correlations among modes instead of particles, providing a different paradigm for quantum information. We prove that the entanglement of almost all states rarely vanishes in the presence of noise, and analyse the most relevant noise in ultracold gases: dephasing and particle losses. Furthermore, when the particle number increases, the entanglement decay can turn from exponential into algebraic.Quantum correlations were proved to be a key resource in quantum information processing [1, 2, 3] and a useful tool for studying condensed matter systems [4,5]. Many of these studies were developed in the framework of distinguishable particles, where particles are manipulated locally. The peculiarity of identical particles is that they cannot be individually addressed, unless particles are effectively distinguished employing additional degrees of freedom [6,7,8], e.g. confining them in different positions.The behaviour of truly identical particles is of practical importance, since they are the elementary constituents of several physical systems in atomic and condensed matter physics. For instance, ultracold gases [9,10,11,12] can be controlled with a very high precision, and are a promising arena for the study of many-body physics and applications in quantum information [13,14,15,16,17,18]. However, these systems are unavoidably affected by noise, typically dephasing and particle losses [9].Despite different approaches [19,20,21,22,8], only a few of them are relevant for observable predictions. The characterization of quantum correlations with identical particles cannot rely on the tensor product structure of single particle Hilbert spaces, but must be reformulated in terms of subsets of locally manipulable observables [23,24,25,26,16,27,28]. This powerful approach generalizes the theory of entanglement of distinguishable particles. Moreover, when applied to identical particles, it accounts for quantum correlations of occupations of orthogonal modes, like wells in optical lattices or hyperfine levels of molecules, which are individually addressable in actual experiments [29,30,31].Within this framework, we shall prove that entanglement of almost all the states is never completely dissipated by noise under minimal assumptions including any Markovian noise, contrary to the case of distinguishable particles. Moreover, entanglement is easily generated by tunneling even in the presence of noise. We shall show with concrete examples that entanglement can decay exponentially in time but is never lost. Interestingly, when the number of particles is very large the exponential decay can turn into an algebraic decay.Beyond the characterization of the dynamics itself, the non-vanishing entanglement of many replicas of states discussed here, though small, can be distilled into a fewer copies of more entagled states via local operations and classical communiation, w...

show abstract

Bipartite entanglement in systems of identical particles: The partial transposition criterion

Cited by 64 publications

References 67 publications

Entanglement and Particle Identity: A Unifying Approach

Entanglement and Particle Identity: A Unifying Approach

The Critical Point Entanglement and Chaos in the Dicke Model

Entanglement in dissipative dynamics of identical particles

Contact Info

Product

Resources

About