Entanglement of indistinguishable particles in condensed-matter physics

Dowling, Mark R.; Doherty, Andrew C.; Wiseman, Howard Mark

doi:10.1103/physreva.73.052323

Cited by 100 publications

(142 citation statements)

References 40 publications

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“…For the Hubbard dimer (a twosite Hubbard model), the authors compare with their results with those for the entanglement measured by the local von Neumann entropy without superselection rule for the local particle numbers . Whereas the latter signals decreasing entanglement in the ground state with increasing U/t, the entanglement of particles increases (Dowling et al, 2006b). This demonstrates that imposing superselection rules may lead to qualitatively different behaviour of the entanglement.…”

Section: E Entanglement Of Particlesmentioning

confidence: 88%

Entanglement in many-body systems

Amico¹,

et al. 2008

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The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

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Section: E Entanglement Of Particlesmentioning

confidence: 88%

Entanglement in many-body systems

Amico¹,

et al. 2008

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“…There, it was suggested to quantify the accessible entanglement entropy S res A by averaging entanglement entropy over super-selection sectors (see also Refs. [84,144,145]). In Ref.…”

Section: Accessible Entropy and Charge Fluctuationsmentioning

confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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“…Attempts at clarification of the various issues that arise when different Bose and Fermi systems with different degrees of freedom are studied [3][4][5][6][7][8][9][10][11][12][13] has led to the examination of various quantities deemed to measure or detect entanglement in the presence of indistinguishability. Here we shall (i) focus on the noninteracting Fermi gas (NIFG) as represented by the three-fermion reduced density matrix of its ground state and (ii) adopt the entanglement witness (EW) criterion [14,15] for analysis of the entanglement content of this tripartite state descriptor, which overcomes disadvantages of some of the earlier work.…”

Section: Introductionmentioning

confidence: 99%

Greenberger-Horne-Zeilinger andWentanglement witnesses for the noninteracting Fermi gas

et al. 2010

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The existence and nature of tripartite entanglement of a noninteracting Fermi gas (NIFG) is investigated. Three new classes of parameterized entanglement witnesses (EWs) are introduced with the aim of detecting genuine tripartite entanglement in the three-body reduced density matrix and discriminating between the presence of the two types of genuine tripartite entanglement, W \ B and GHZ \ W . By choosing appropriate EW operators, the problem of finding GHZ and W EWs is reduced to linear programming. Specifically, we devise new W EWs based on a spin-chain model with periodic boundary conditions, and we construct a class of parametrized GHZ EWs by linearly combining projection operators corresponding to all the different state-vector types arising for a three-fermion system. A third class of EWs is provided by a GHZ stabilizer operator capable of distinguishing W \B from GHZ \B entanglement, which is not possible with W EWs. Implementing these classes of EWs, it is found that all states containing genuine tripartite entanglement are of W type, and hence states containing GHZ \ W genuine tripartite entanglement do not arise. Some genuine tripartite entangled states that have a positive partial transpose (PPT) with respect to some bipartition are detected. Finally, it is demonstrated that a NIFG does not exhibit "pure" W \ B genuine tripartite entanglement: three-party entanglement without any separable or biseparable admixture does not occur.

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Entanglement of indistinguishable particles in condensed-matter physics

Cited by 100 publications

References 40 publications

Entanglement in many-body systems

Entanglement in many-body systems

Bipartite fluctuations as a probe of many-body entanglement

Greenberger-Horne-Zeilinger andWentanglement witnesses for the noninteracting Fermi gas

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