Violation of the Lüders bound of macrorealist and noncontextual inequalities

Kumari, Anupma; Qutubuddin, Md.; Pan, A. K.

doi:10.1103/physreva.98.042135

Cited by 21 publications

(23 citation statements)

References 61 publications

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“…The post measurement state remains same for both the case of using Lüders and von Neumann state update rule and hence Cirelson's bound is the maximum achievable bound. Note that, we have recently questioned the implication of von Neumann projection rule for the cases of the violation of Lüders bound of Leggett-Garg inequalities and non-contextual inequalities [13]. We argued that, the quantum violation of Leggett-Garg inequalities by invoking the von Neumann rule should not be treated as the traditional notion for the quantum violation Leggett-Garg inequalities.…”

Section: Introductionmentioning

confidence: 98%

L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality

Kumari,

Pan

2020

Preprint

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Section: Introductionmentioning

confidence: 98%

L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality

Kumari,

Pan

2020

Preprint

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“…The post measurement state remains same for both the case of using L üders and von Neumann state update rule and hence Cirelson's bound is the maximum achievable bound. Note that, we have recently questioned the implication of von Neumann projection rule for the cases of the violation of L üders bound of Leggett-Garg inequalities and non-contextual inequalities [12]. We argued that, the quantum violation of Leggett-Garg inequalities by invoking the von Neumann rule should not be treated as the traditional notion for the quantum violation Leggett-Garg inequalities.…”

Section: Introductionmentioning

confidence: 98%

L$\ddot {u}$der Rule, Von Neumann Rule and Cirelson’s Bound of Bell CHSH Inequality

Kumari

Pan

2021

Int J Theor Phys

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In Budroni and Emary (Phys. Rev. Lett. 113, 050401, 2014) the authors have shown that instead of L üder rule, if degeneracy breaking von Neumann projection rule is adopted for state reduction, the quantum value of three-time Leggett-Garg inequality can exceed it's L üders bound. Such violation of L üders bound may even approach algebraic maximum of the inequality in the asymptotic limit of system size. They also claim that for Clauser-Horne-Shimony-Holt (CHSH) inequality such violation of L üders bound (known as Cirelson's bound) cannot be obtained even when the measurement is performed sequentially first by Alice followed by Bob. In this paper, we have shown that if von Neumann projection rule is used, quantum bound of CHSH inequality exceeds it's Cirelson's bound and may also reach its algebraic maximum four. This thus provide a strong objection regarding the viability of von Neumann rule as a valid state reduction rule. Further, we pointed out that the violation of Cirelson's bound occurs due to the injection of additional quantum non-locality by the act of implementing von Neumann rule.

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“…The maximum quantum bound of K 3 for an N level system is 3/2 which is known Lüders bound [11]. Violation of this bound for an N level quantum system, where N > 2 is possible provided further degeneracy breaking measurements are performed [11,12] but the violation of Lüders bound for N = 2 i.e. a two level system (TLS) is impossible within the unitary dynamics.…”

Section: Introductionmentioning

confidence: 99%

Leggett-Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath

Ghosh¹,

V.²,

Das³

2021

Preprint

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We study Leggett-Garg inequalities (LGIs) for a two level system (TLS) undergoing Markovian dynamics described by unital maps. We find analytic expression of LG parameter K3 (simplest variant of LGIs) in terms of the parameters of two distinct unital maps representing time evolution for intervals: t1 to t2 and t2 to t3. We show that the maximum violation of LGI for these maps can never exceed well known Lüders bound of K Lüders 3 = 3/2 over the full parameter space. We further show that if the map for the time interval t1 to t2 is non-unitary unital then irrespective of the choice of the map for interval t2 to t3 we can never reach Lüders bound. On the other hand, if the measurement operator eigenstates remain pure upon evolution from t1 to t2, then depending on the degree of decoherence induced by the unital map for the interval t2 to t3 we may or may not obtain Lüders bound. Specifically, we find that if the unital map for interval t2 to t3 leads to the shrinking of the Bloch vector beyond half of its unit length, then achieving the bound K Lüders 3 is not possible. Hence our findings not only establish a threshold for decoherence which will allow for K3 = K Lüders 3 , but also demonstrate the importance of temporal sequencing of the exposure of a TLS to Markovian baths in obtaining Lüders bound.

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Violation of the Lüders bound of macrorealist and noncontextual inequalities

Cited by 21 publications

References 61 publications

L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality

L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality

L$\ddot {u}$der Rule, Von Neumann Rule and Cirelson’s Bound of Bell CHSH Inequality

Leggett-Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath

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