RotationalInvariance as an Additional Constraint on Local Realism

Nagata, Koji; Laskowski, Wiesław; Wieśniak, Marcin; Żukowski, Marek

doi:10.1103/physrevlett.93.230403

Cited by 34 publications

(51 citation statements)

References 10 publications

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“…Since C is invariant under local unitary operations (local rotations) [27], and the random correlations are the average of C over random rotations applied to local bases x, y, z, it is merely a mathematical step to obtain:…”

Section: Random Correlationsmentioning

confidence: 99%

“…Instead of averaging over random u n , R can also be estimated from correlations along orthogonal local directions x, y, z. Let us introduce a quantity which we refer to as the length of correlations:Since C is invariant under local unitary operations (local rotations) [27], and the random correlations are the average of C over random rotations applied to local bases x, y, z, it is merely a mathematical step to obtain:where the factor of 1/3 for every observer takes into account the fact that rotating one axis over a 4π solid angle also makes the other two axes rotate over a 4π solid angle. The following theorem shows a universal lower bound on the random correlations in every pure state |ψ of N qubits.…”

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confidence: 99%

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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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Section: Random Correlationsmentioning

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Quantum entanglement from random measurements

et al. 2015

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“…One can show that every vertex of the convex polytope, V abcd,x , saturates the left or right hand side inequality in (17)involving the sign admissible sign function S. Since the inequalities are linear, therefore they must be satisfied by any convex combination of the vertices.…”

Section: B Necessary Conditionmentioning

confidence: 99%

“…We shall not follow this approach here, as it seems to be incapable of generating the full set of Bell inequalities. Also the methods of [16] and [17] will be not discussed here, as they do not follow from the analysis of the geometry of the polytope of local realistic models (for this concept see [18]). …”

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On Tight Multiparty Bell Inequalities for Many Settings

Żukowski

2006

Quantum Inf Process

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“…The results of first argumentation, dealing with consequences for the assumption of rotational invariance for tests of non-locality, have been published [3]- [5]. Our intention is to engage with and expand upon these same results with mixture of ten-particle Greenberger-Horne-Zeilinger (GHZ) state [6].…”

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Whether the CPT Symmetry Can Be Almighty Even in a Photon

Nagata¹,

Nakamura²

2015

OALib

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As a trial, though thinking of general concepts, of our scientific challenge, we consider whether the Charge-Parity-Time (CPT) symmetry can be almighty even in a photon. This is the main aim of this paper. In what follows, we discuss our argumentations dividing the conjecture into two parts. Rotational invariance of physical laws is an accepted principle in Newton's theory. We show that it leads to an additional constraint on local realistic theories with mixture of ten-particle GreenbergerHorne-Zeilinger state. This new constraint rules out such theories even in some situations in which standard Bell inequalities allow for explicit construction of such theories. This says new hypothesis to the number of ten. Next, it turns out Zermelo-Fraenkel set theory has contradictions. Further, the von Neumann's theory has a contradiction by using ±1. We solve the problem of von Neumann's theory while escaping from all contradictions made by Zermelo-Fraenkel set theory, simultaneously. We assume that the results of measurements are 1 2 ± . We assume that only E 1 2 = and E 1 2 = − are possible. This situation meets a structure made by Zermelo-Fraenkel set theory with the axiom of choice. We result in the fact that it may be kept to perform the Deutsch-Jozsa algorithm even in the macroscopic scale because zero does not exist in this case. Our analysis agrees with recent experimental report.

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RotationalInvariance as an Additional Constraint on Local Realism

Cited by 34 publications

References 10 publications

Quantum entanglement from random measurements

Quantum entanglement from random measurements

On Tight Multiparty Bell Inequalities for Many Settings

Whether the CPT Symmetry Can Be Almighty Even in a Photon

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