Bell inequality for pairs of particle-number-superselection-rule restricted states

Heaney, Libby; Lee, Seung-Woo; Jaksch, Dieter

doi:10.1103/physreva.82.042116

Cited by 12 publications

(17 citation statements)

References 51 publications

(100 reference statements)

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“…States as in (53) are separable-III for they are isomorphic to |0 ⊗k ⊗ |1 ⊗(N −k) ∈ h k ⊗ h N −k , according to equation (70) in A. Thus, states in quantum protocols with two-level particles cannot, at any time during the process, be entangled-III although these states provide quantum enhanced performances not only for interferometric phase estimation [151,152,153,174,154,175] but also for teleportation [176,177,178,179,114,115], entanglement distillation [176,177], quantum data hiding [180], and Bell's inequalities [181,182,183,184,185,186,187,188,189,190,191,192,193]. The same argument holds for three-level states.…”

Section: Information Resourcesmentioning

confidence: 99%

Entanglement in indistinguishable particle systems

et al. 2020

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For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the indistinguishability of identical particles hinders their individual addressability and has prompted diverse, sometimes discordant definitions of entanglement. In the present review, we provide a comparative analysis of the relevant existing approaches, which is based on the characterization of bipartite entanglement in terms of the behaviour of correlation functions. Such a a point of view provides a fairly general setting where to discuss the presence of non-local effects; it is performed in the light of the following general consistency criteria: i) entanglement corresponds to non-local correlations and cannot be generated by local operations; ii) when, by "freezing" suitable degrees of freedom, identical particles can be effectively distinguished, their entanglement must reduce to the one that holds for distinguishable particles; iii) in absence of other quantum resources, only entanglement can outperform classical information protocols. These three requests provide a setting that allows to evaluate strengths and weaknesses of the existing approaches to indistinguishable particle entanglement and to contribute to the current understanding of such a crucial issue. Indeed, they can be classified into five different classes: four hinging on the notion of particle and one based on that of physical modes. We show that only the latter approach is consistent with all three criteria, each of the others indeed violating at least one of them.

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Section: Information Resourcesmentioning

confidence: 99%

Entanglement in indistinguishable particle systems

et al. 2020

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“…The properties of entanglement have been studied in Fermionic superconducting systems [29,30], electrons in low-dimensional semiconductors [31], and bosonic ultracold gases [22,[32][33][34][35], and exploited in several applications, such as quantum data hiding [36], teleportation [37][38][39][40][41], Bell's inequalities [42,43], dense coding [39], and quantum metrology [22,25,34,35]. Since quantum teleportation is a primitive for scalable quantum computers [44], and plays a fundamental role in measurement-based quantum computation [45,46], we will focus on this special topic hereafter.…”

Section: Introductionmentioning

confidence: 99%

Performances and robustness of quantum teleportation with identical particles

Marzolino

Buchleitner

2016

Proc. R. Soc. A.

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When quantum teleportation is performed with truly identical massive particles, indistinguishability allows us to teleport addressable degrees of freedom which do not identify particles, but, for example, orthogonal modes. The key resource of the protocol is a state of entangled modes, but the conservation of the total number of particles does not allow for perfect deterministic teleportation unless the number of particles in the resource state goes to infinity. Here, we study the convergence of teleportation performances in the above limit and provide sufficient conditions for asymptotic perfect teleportation. We also apply these conditions to the case of resource states affected by noise.

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“…The CHSH Bell inequality purposed in [12] for pairs of states restricted with the particle-number-superselection rule is given by…”

Section: Steering Inequalitymentioning

confidence: 99%

“…Table I: [This table is given in Ref. [12].] When we make a measurement on the modes c and C on Alice's side, in the particle number basis, an effective measurement is carried out on Alice's side in the modes a and A.…”

Section: Non-interacting Bose-einstein Condensate Statesmentioning

confidence: 99%

“…A straightforward testing of Bell's inequality may not be possible for systems of indistinguishable particles, since rotations away from fixed particle number bases may not be allowed due to the restriction imposed by a superselection rule on indistinguishable systems [5][6][7][8][9][10][11]. Interestingly, Heaney, Lee, and Jaksch [12] derived a method for testing Bell inequalities for states of indistinguishable particles even within the superselection-rule restrictions. In order to overcome the superselection rule, they use two copies of system for performing rotated measurements.…”

Section: Introductionmentioning

confidence: 99%

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Steering inequality for pairs of particle-number-superselection-rule restricted states

Kumari¹,

Sen²

2021

Preprint

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We consider violations of a Clauser-Horne-Shimony-Holt-type steering inequality for quantum states of systems of indistinguishable particles restricted by a particle-number-superselection rule. We check for violations in non-interacting Bose-Einstein condensate and N00N states, by using twocopies of the states for bypassing the superselection rule. The superselection rule prevents the states from maximally violating the steering inequality. But the steering inequality violations are higher than Bell inequality violations for the same states. This in particular implies, in certain cases, that visibilities of the steering inequality violations are higher than the same for Bell inequality violations, for admixtures with white noise. We also found that an increase in the number of particles in the non-interacting condensate states results in a decrease of the violation amount of the steering inequality.

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Bell inequality for pairs of particle-number-superselection-rule restricted states

Cited by 12 publications

References 51 publications

Entanglement in indistinguishable particle systems

Entanglement in indistinguishable particle systems

Performances and robustness of quantum teleportation with identical particles

Steering inequality for pairs of particle-number-superselection-rule restricted states

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