Joint measurements of spin, operational locality, and uncertainty

Andersson, Erika; Barnett, Stephen M.; Aspect, Alain

doi:10.1103/physreva.72.042104

Cited by 58 publications

(98 citation statements)

References 26 publications

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“…If, however, we require that a joint quantum mechanical measurement of spin along both directions a 1 and b 1 is made on the first spin 1/2 particle, then the CHSH inequality will always be satisfied for the resulting measurement results [8,9]. In this case, there are simultaneous results a 1 and b 1 , as well as either a 2 or b 2 , for each experimental run.…”

Section: The Chsh Inequalitymentioning

confidence: 99%

“…An earlier work [8] investigated the connection between the joint measurements of a spin along two directions and the CHSH Bell inequalities, as well as the increase in uncertainty for the jointly measured observables. In the following Section, we review the derivation of the CHSH inequality and its connection with joint measurements.…”

Section: Joint Measurements Of Non-commuting Observablesmentioning

confidence: 99%

“…In an earlier paper [8], the connection between the restrictions placed on joint quantum measurements and the Clauser-Horne-Shimony-Holt (CHSH) inequality [10] were investigated. In the CHSH setup, one considers a pair of spin 1/2 particles; on each one, one makes a choice of measuring a spin along one of two possible directions.…”

Section: Introductionmentioning

confidence: 99%

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Joint measurements and Bell inequalities

Son¹,

Andersson²,

Barnett³

et al. 2005

Phys. Rev. A

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Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the threeparticle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three co-planar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

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Section: The Chsh Inequalitymentioning

confidence: 99%

Section: Joint Measurements Of Non-commuting Observablesmentioning

confidence: 99%

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Joint measurements and Bell inequalities

Son¹,

Andersson²,

Barnett³

et al. 2005

Phys. Rev. A

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“…This we have shown with the help of (a) POVM formalism of quantum mechanics which limits to what extent one can simultaneously measure two non commuting observables in quantum mechanics and (b) an inequality due to Anderson et al [10] derived under the assumptions of existence of joint measurement and nonexistence of superluminal signalling in a physical theory. Fortunately, the bound on correlation function under this newer (than the original localrealistic) assumptions and the bound on correlation function under the assumption of local-realism, come out to be same; i.e.…”

Section: Discussionmentioning

confidence: 99%

“…al [10] have derived Bell's inequality by assuming the existence of joint measurement (not necessarily revealing the pre-existing value) and no signalling condition. This is not a trivial assumption.…”

Section: Joint Measurement No Signalling and Bell's Inequalitymentioning

confidence: 99%

Causality, joint measurement and Tsirelson's bound

et al. 2007

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Tsirelson showed that 2 √ 2 is the maximum value that CHSH expression can take for quantumcorrelations [B. S. Tsirelson Lett. Math. Phys. 4, (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S. Massar Phys. Rev. A 72, (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality which has been derived under the assumption of existence of joint measurement and no signalling condition. IntroductionThere exists quantum-mechanical states shared between two parties which exihibit nonlocal character. This nonlocality is quantified by using 'Bell's expression'. This is an expression which is bounded by a certain value for 'Local Hidden Variable (LHV) models'; but can exceed this value in case of quantum correlations. Consider for example a setting of two parties, Alice and Bob; sharing a quantum state ρ and each has a choice of two local measurements. Alice can measure the observables A and A ′ whereas Bob's observables are B and B ′ . The measured values of all the obsevables can be 1 or -1. One relevant Bell's expression in this case is the Clauser-Horn-Shimony-Holt (CHSH) expression [2]. For local hidden varriable models, this expression is bounded by 2 but in case of entangled quantum systems,this bound can be violated. For example, on the singlet state of two qubits there exist observables (A,A ′ ,B,B ′ )for which value of the above expression is 2 √ 2. In fact as shown later by Tsirelson [3] that 2 √ 2 is the maximum quantum value of the 1 CHSH expression.Tsirelson's bound is a simple mathematical consequence of the axioms of quantum theory, but it would be interesting to know that whether there is some deeper reason why a violation greater than 2 √ 2 is unphysical. It is known in this connection that a violation greater than 32 3 ≃ 3.27 would imply that any communication complexity problem can be solved using a constant amount of communication [4].But this does not answer the question that what odd would have happened for a violation just greater than 2 √ 2. Recently by exploiting the physical structure of quantum mechanics like unitary dynamics and linearity; Buhrman and Massar [1] have shown that exceeding Tsirelson's bound by quantum mechanics will imply signalling in quantum mechanics. Here we provide a simple proof of the same by exploiting nice results of existence of joint measurement for spin along two different directions in quantum mechanics [5,6,7,8,9] and a Bell's inequality derived under assumptions different than that of the local-realism. Joint measurement, No signalling and Bell's InequalityUsually, Bell's inequality is derived under the notion of local-realism. So, its violation by a theory will imply that the theory is incompatible with the notion of local-realism. For example, ...

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On Peculiar Relations Between Measurement Incompatibility and Contextuality

Kaszlikowski

Kurzyński

2017

Quantum Interaction

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Joint measurements of spin, operational locality, and uncertainty

Cited by 58 publications

References 26 publications

Joint measurements and Bell inequalities

Joint measurements and Bell inequalities

Causality, joint measurement and Tsirelson's bound

On Peculiar Relations Between Measurement Incompatibility and Contextuality

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