Weak values in a classical theory with an epistemic restriction

Karanjai, Angela; Cavalcanti, Eric G.; Bartlett, Stephen D.; Rudolph, Terry

doi:10.1088/1367-2630/17/7/073015

Cited by 17 publications

(27 citation statements)

References 29 publications

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“…In other words, if we measure disturbance using p d then, contrary to the claim in parenthesis in the quotation above, the weak measurements considered in Ref. [13] do not have the favorable informationdisturbance tradeoff needed to prove contextuality.…”

Section: The Status Of Imaginary Weak Valuesmentioning

confidence: 82%

“…Hence, if Eqs. (12) and (13) were verified (only Eq. (12) is claimed), the experiment would be a proof of contextuality from AWV.…”

Section: Awv and Contextuality Beyond Idealisationsmentioning

confidence: 99%

“…This amount of disturbance is, unsurprisingly, bounded by the p d from Eq. (13). We then actually sample x from the operational distribution for y = λ , the disturbed ontic state, which is why Eq.…”

Section: Necessity Of Conditionmentioning

confidence: 99%

“…Salek for useful discussions, particularly regarding the imaginary parts of weak values, and disturbance in Ref. [13]. ML thanks The channel induced by the weak measurement when the outcome is not recorded is…”

Section: Mp Thanks Jonathan Barrett and Sinamentioning

confidence: 99%

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Anomalous weak values and contextuality: Robustness, tightness, and imaginary parts

2019

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Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401, arXiv:1409.1535]. Here we elaborate on and extend that result in several directions. Firstly, the original theorem requires certain perfect correlations that can never be realised in any actual experiment. Hence, we provide new theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values, and compare with a recent experiment. Secondly, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight -if any one of them is dropped, the anomaly can be reproduced classically. Thirdly, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.1 Note that one can have instances in which some or all φ E i ρ are anomalous, but φ O ρ is not, e.g. if an observable has a zero eigenvalue then the weak value of the associated projector is irrelevant to the weak value of the observable.

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Section: The Status Of Imaginary Weak Valuesmentioning

confidence: 82%

“…Hence, if Eqs. (12) and (13) were verified (only Eq. (12) is claimed), the experiment would be a proof of contextuality from AWV.…”

Section: Awv and Contextuality Beyond Idealisationsmentioning

confidence: 99%

Section: Necessity Of Conditionmentioning

confidence: 99%

Section: Mp Thanks Jonathan Barrett and Sinamentioning

confidence: 99%

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Anomalous weak values and contextuality: Robustness, tightness, and imaginary parts

2019

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“…classical) model [14,117]. Similarly, anomalous values, which have been attributed much physical significance [109,110], occur as statistical anomalies in classical weak value models [118], typically in conjunction with measurement disturbance [114,[118][119][120][121].…”

Section: Weak Valuesmentioning

confidence: 99%

Exploring quantum foundations with single photons

Ringbauer¹

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Quantum mechanics is our most successful physical theory and has been confirmed to extreme accuracy, yet, a century after its inception it is still unclear what it says about the nature of reality. In this thesis, I explore some of the foundational questions which are central to our understanding of quantum mechanics using single photons as an experimental platform. Three experiments form the core of the thesis, studying, respectively, the role of reality, causality, and uncertainty in quantum mechanics. These experiments shed light on decade-old questions that have previously been thought to be outside the realm of experimental physics. The results contribute to our understanding of the structure of quantum mechanics, and reveal novel aspects of phenomena that were believed to be well understood. In three further experiments I also touch upon the topics of finding physical principles behind quantum mechanics, quantum effects in extreme gravitational fields, and developing a pathway towards tests of macroscopic quantum phenomena. Starting out as a fringe discipline, the field of quantum foundations has developed into an influential area of research. It is now becoming possible to turn many of the foundational questions in quantum mechanics from topics of philosophy into topics of physics. Subjecting these questions to rigorous experimental tests the field is making progress in the quest for understanding our best physical theory.i Declaration by authorThis thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis.I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award.I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School.I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis.ii Publications during candidaturePeer-re...

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How (Maximally) Contextual Is Quantum Mechanics?

Simmons

2020

Jerusalem Studies in Philosophy and History of Science

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Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors must have a valuation that depends on the context in which they are measured. This motivates the question of how many of the projectors must have contextual valuations. In this paper, we demonstrate a bound on what fraction of rank-1 projective measurements on a quantum system must be considered to have context-dependent valuations as a function of the quantum dimension, and show that quantum mechanics is not as contextual, by this metric, as other possible physical theories. Attempts to find quantum mechanical scenarios that yield a high value of this figure-of-merit can be thought of as generalisations or extensions of the search for small Kochen-Specker sets. We also extend this result to projector-valued-measures with projectors of arbitrary equal rank.

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Weak values in a classical theory with an epistemic restriction

Cited by 17 publications

References 29 publications

Anomalous weak values and contextuality: Robustness, tightness, and imaginary parts

Anomalous weak values and contextuality: Robustness, tightness, and imaginary parts

Exploring quantum foundations with single photons

How (Maximally) Contextual Is Quantum Mechanics?

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