Unsharp reality and joint measurements for spin observables

Busch, Paul

doi:10.1103/physrevd.33.2253

Cited by 280 publications

(349 citation statements)

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“…It has been shown [15] that if tr[ρE] ≥ 1 − ε, then φ E L does not decrease this probability and the state change, measured by the trace-norm distance, is small to the order of √ ε. This demonstrates the stability of the EPR reality criterion against small deviations from actualization, and one may say that approximately real properties can be ascertained almost with certainty and without significantly altering the system.…”

Section: 4mentioning

confidence: 99%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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ABSTRACT. The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it a concept of joint properties. A property manifests itself as an element of unsharp reality by its power, or tendency, of becoming actual or actualizing a specific measurement outcome, where this tendency of actualization is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

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Section: 4mentioning

confidence: 99%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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“…But in the more general framework, it has been shown that certain complementary observables (in standard measurement) can be measured jointly if they are represented by a particular form of POVM (having an interpretation in terms of unsharpness) instead of being represented by projection operators [5,6]. Joint measurement of spin observables in different directions has been extensively studied by P. Busch [7]. He, by exploiting the necessary and sufficient condition for co-existence of two effects as given by Kraus [5], showed that a pair of unsharp spin properties E λ 1 (α 1 )and E λ 2 (α 2 )are co-existent (i.e.…”

Section: Existence Of Joint Measurement In Quantum Mechanicsmentioning

confidence: 99%

“…In the case of spin-1/2 particles, P. Busch [7,8] had first introduced collection of positive operators with the above said properties in a particular form which can be interpreted as unsharp spin observables. This particular unsharp observables are represented in the following form :…”

Section: Quantum Measurementsmentioning

confidence: 99%

“…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. …”

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confidence: 99%

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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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“…22 Pairs of unsharp observables of the form (26) are probabilistically complementary but in general not complementary. We may derive a simple geometric criterion for the coexistence of such observables.…”

Section: Proposition Noncoexistent Observables Do Not Admit Any Jmentioning

confidence: 99%

Prospects of ultra-relativistic heavy-ion collisions

Waheed

Furlan

1995

Riv. Nuovo Cim.

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Three notions of complementarity -operational, probabilistic, and value complementarity -are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables. It is shown that the joint measurability of noncommuting observables is a consequence of the quantum formalism if unsharp observables are taken into account; a fact not in conflict with the idea of complementarity, which, in its strongest version, was originally formulated only for sharp observables. As an illustration of the general theory, the wave-particle duality of photons is analysed in terms of complementary path and interference observables and their unsharp joint measurability.

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Unsharp reality and joint measurements for spin observables

Cited by 280 publications

References 19 publications

Unsharp Quantum Reality

Unsharp Quantum Reality

Causality, joint measurement and Tsirelson's bound

Prospects of ultra-relativistic heavy-ion collisions

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