Optimal reference states for maximum accessible entanglement under the local-particle-number superselection rule

White, Graham; Vaccaro, John A.; Wiseman, Howard Mark

doi:10.1103/physreva.79.032109

Cited by 11 publications

(13 citation statements)

References 35 publications

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“…The consequences of Definition 5 have been sudied by several authors [155,156,120,157,158,159,160,161,162,163,164,165,166], and applied in particular to condensed matter systems [167,168,169,170,171] The motivation for this formulation of particle-entanglement originates from a rather specific physical setting requiring information transmission from a system of identical particles to a quantum register made of distinguishable qubits, usually described by tensor products of single-particle Hilbert spaces with fixed numbers of particles in suitably chosen subgroups. This condition on one hand confirms that the locality criterion underlying entanglement-III is also related to the particle picture as in Definition 2 and, on the other hand, that it can be implemented by selecting degrees of freedom and corresponding observables associated with the confinement of individual particle states to orthogonal subspaces, say V 1 and V 2 , of the single-particle Hilbert space.…”

Section: Entanglement-iiimentioning

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: Entanglement-iiimentioning

confidence: 99%

Entanglement in indistinguishable particle systems

et al. 2020

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“…Individually both of these questions have been addressed before. It is known that entanglement can be detected, cryptography can be realised, and Bell inequalities can be violated without a shared reference frame [1][2][3][4][5][6][7][8][9][10][11][12][13] and non-classical correlations can also be observed with finite-size references which are to some degree correlated [14][15][16]. Here we simultaneously address both questions and show that observers who have independent reference frames in an unknown state can each use a single spin- 1 2 of the reference per experimental run in order to detect entanglement.…”

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confidence: 99%

Quantum entanglement from random measurements

et al. 2015

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We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states which can be directly experimentally assessed if two copies of the state were available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarisers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and in fact observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasise how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilised randomness and should find practical applications in experimental confirmation of multi-photon entanglement or space experiments.PACS numbers: 03.65.UdQuantum mechanics imposes no limits on the spatial separation between entangled particles. This naturally leads one to ask whether observers that have never met and do not share a common reference frame can still detect effects of quantum entanglement. One can further ask if in every experimental run each observer's local reference frame needs to be composed of a huge number of somewhat correlated elementary systems (as it is the case for Stern-Gerlach magnets, polarisers, etc.), or if the effects of entanglement can be detected with references composed of only a few systems.Individually both of these questions have been addressed before. It is known that entanglement can be detected, cryptography can be realised, and Bell inequalities can be violated without a shared reference frame [1][2][3][4][5][6][7][8][9][10][11][12][13] and non-classical correlations can also be observed with finite-size references which are to some degree correlated [14][15][16]. Here we simultaneously address both questions and show that observers who have independent reference frames in an unknown state can each use a single spin-1 2 of the reference per experimental run in order to detect entanglement. If the state of the reference can be controlled a single spin-1 2 of it per experimental run will be shown to be sufficient to observe all phenomena that one can observe with macroscopic references in every experimental run.These findings have both practical and fundamental aspects. On the practical side, they show that entanglement detection is possible with independent reference frames and hence observers can save on communication resources [17][18][19][20] or pre-established quantum entanglement [21,22] that would have to be consumed to correlate local reference frames. On the fundamental side, bounded reference frames were discussed in the context of quantum-to-classical transition [14], where it was noted that the lack of perfect reference frames leads to "intrinsic ...

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“…Challenges to the requirement for quantum states to be consistent with superselection rules have occured since the 1960's when Aharonov and Susskind [59] suggested that coherent superpositions of different charge eigenstates could be created. It is argued that super-selection rules are not a fundamental requirement of quantum theory, but the restrictions involved could be lifted if there is a suitable system that acts as a reference for the coherences involved - [59], [60], [61], [62], [63], [64], [53], [56], [57], [34] provide discussions regarding reference systems and SSR.…”

Section: Reference Frames and Violations Of Superselection Rulesmentioning

confidence: 99%

Quantum entanglement for systems of identical bosons: I. General features

et al. 2017

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These two accompanying papers are concerned with two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems in which the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. There are many aspects of entanglement that can be studied. This two-part review focuses on the meaning of entanglement, the quantum paradoxes associated with entangled states, and the important tests that allow an experimentalist to determine whether a quantum state -in particular, one for massive bosons is entangled. An overall outcome of the review is to distinguish criteria (and hence experiments) for entanglement that fully utilise the symmetrisation principle and the super-selection rules that can be applied to bosonic massive particles.In the first paper (I), the background is given for the meaning of entanglement in the context of systems of identical particles. For such systems, the requirement is that the relevant quantum density operators must satisfy the symmetrisation principle and that global and local super-selection rules prohibit states in which there are coherences between differing particle numbers. The justification for these requirements is fully discussed. In the second quantisation approach that is used, both the system and the sub-systems are modes (or sets of modes) rather than particles, particles being associated with different occupancies of the modes. The definition of entangled states is based on first defining the non-entangled states -after specifying which modes constitute the sub-systems. This work mainly focuses on the two mode entanglement for massive bosons, but is put in the context of tests of local hidden variable theories, where one may not be able to make the above restrictions. The review provides the detailed arguments necessary for the conclusions of a recent paper, where the question of how to rigorously demonstrate the entanglement of a two-mode Bose-Einstein condensate (BEC) has been examined.In the accompanying review paper (II), we consider spin squeezing and other tests for entanglement that have been proposed for two-mode bosonic systems. We apply the approach of review (I) to determine which tests, and which modifications of the tests, are useful for detecting entanglement in massive bosonic (BEC), as opposed to photonic, systems. Several new inequalities are derived, a theory for the required two-mode interferometry is presented, and key experiments to date are analysed.

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Optimal reference states for maximum accessible entanglement under the local-particle-number superselection rule

Cited by 11 publications

References 35 publications

Entanglement in indistinguishable particle systems

Entanglement in indistinguishable particle systems

Quantum entanglement from random measurements

Quantum entanglement for systems of identical bosons: I. General features

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