The Role of Bounded Memory in the Foundations of Quantum Mechanics

Cabello, Adán

doi:10.1007/s10701-010-9507-2

Cited by 8 publications

(9 citation statements)

References 36 publications

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“…Indeed, according to postulate 2, sinceσ x ⊗σ x (|00 + |11 ) / √ 2 = 1 (|00 + |11 ) / √ 2, M 3 (Â 13 ) = 1 for all allowed values of c. It is to be noted that M 2 (Â 33 ) = M 3 (Â 33 ) and M 2 (Â 23 ) = M 3 (Â 23 ), which essentially expresses the compatibility of these observables; i.e. once measured, the values of observables compatible withÂ 13 are not affected by the measurement ofÂ 13 .…”

Section: Assignment or Predictionmentioning

confidence: 90%

“…Contextuality has thus been identified as a fundamental non-classical feature of the quantum world and experiments have also been proposed and conducted to this effect [10,11]. Contextuality, on the one hand has led to investigations on the foundational aspects of QM including attempts to prove the completeness of QM [12,13], and on the other hand has been harnessed for computation and cryptography [14,15]. While there have been generalisations, in this letter, we restrict ourselves to the standard notion of non-contextuality as used by KS [6].…”

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confidence: 99%

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Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

2019

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We construct a non-contextual hidden variable model consistent with all the kinematic predictions of quantum mechanics (QM). The famous Bell-KS theorem shows that non-contextual models which satisfy a further reasonable restriction are inconsistent with QM. In our construction, we define a weaker variant of this restriction which captures its essence while still allowing a non-contextual description of QM. This is in contrast to the contextual hidden variable toy models, such as the one by Bell, and brings out an interesting alternate way of looking at QM. The results also relate to the Bohmian model, where it is harder to pin down such features.

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Section: Assignment or Predictionmentioning

confidence: 90%

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confidence: 99%

Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

2019

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“…When pairs of measurements are conducted simultaneously, it is difficult to establish an operational definition of an individual measurement [22]. It has been argued that this so-called "individual existence loophole" can be addressed by performing measurements in a sequence [49].…”

Section: Appendix J: Comparison With Previous Kcbs Testsmentioning

confidence: 99%

Probing the limits of correlations in an indivisible quantum system

et al. 2018

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We employ a trapped ion to study quantum contextual correlations in a single qutrit using the 5-observable KCBS inequality, which is arguably the most fundamental non-contextuality inequality for testing Quantum Mechanics (QM). We quantify the effect of systematics in our experiment by purposely scanning the degree of signaling between measurements, which allows us to place realistic bounds on the non-classicality of the observed correlations. Our results violate the classical bound for this experiment by up to 25 standard deviations, while being in agreement with the QM limit. In order to test the prediction of QM that the contextual fraction increases with the number of observables, we gradually increase the complexity of our measurements from 5 up to 121 observables. We find stronger-than-classical correlations in all prepared scenarios up to 101 observables, beyond which experimental imperfections blur the quantum-classical divide.

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“…-Any member of EXPPromiseTWINPAL yes is accepted with probability at least 16 25 1 − 1 e . So, LV EX PT WIN PAL gives the decision "don't know" with a probability no more than 9 25 + 16 25e . -Any member of EXPPromiseTWINPAL no is rejected with probability at least 9 25 1 − 1 e .…”

Section: E the Proof Of Theoremmentioning

confidence: 99%

Implications of Quantum Automata for Contextuality

Rashid

Yakaryılmaz

2014

Implementation and Application of Automata

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Abstract. We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results:1. There is a promise problem solvable by an exact two-way QFA in exponential expected time, but not by any bounded-error sublogarithmic space probabilistic Turing machine (PTM). 2. There is a promise problem solvable by an exact two-way QFA in quadratic expected time, but not by any bounded-error o(log log n)-space PTMs in polynomial expected time. The same problem can be solvable by a one-way Las Vegas (or exact two-way) QFA with quantum head in linear (expected) time. 3. There is a promise problem solvable by a Las Vegas realtime QFA, but not by any bounded-error realtime PFA. The same problem can be solvable by an exact two-way QFA in linear expected time but not by any exact two-way PFA. 4. There is a family of promise problems such that each promise problem can be solvable by a two-state exact realtime QFAs, but, there is no such bound on the number of states of realtime bounded-error PFAs solving the members this family. Our results imply that there exist zero-error quantum computational devices with a single qubit of memory that cannot be simulated by any finite memory classical computational model. This provides a computational perspective on results regarding ontological theories of quantum mechanics [19], [30]. As a consequence we find that classical automata based simulation models [23], [6] are not sufficiently powerful to simulate quantum contextuality. We conclude by highlighting the interplay between results from automata models and their application to developing a general framework for quantum contextuality.

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The Role of Bounded Memory in the Foundations of Quantum Mechanics

Cited by 8 publications

References 36 publications

Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

Probing the limits of correlations in an indivisible quantum system

Implications of Quantum Automata for Contextuality

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