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Weak Measurement and TSVF

K.G.M. Orbons

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this thesis, the article “Can a Future Choice Affect a Past Measurement’s\nOutcome?” is used as a starting point to explore the peculiar\ncorrelations between subsequent weak (i.e. non-projective) and\nstrong measurements in a variation of the EPR-Bell experiment. Bell’s\ntheorem states that particles may not possess predetermined values.\nHowever, as the outcomes of the subsequent weak and strong measurements\ndo statistically agree, an apparent contridiction arises. The\nauthors claim that the correlations between the results are best explained\nusing the time-symmetric two-state vector formalism, stating\nthat the experimenter’s future choice has been encrypted in the weak\nmeasurement’s outcomes.\nAlternative explanations are analyzed and a numerical simulation was\nmade to invigorate the notion of a so called weak-bias. Meaning that\nthe weak measurements sufficiently influence the particles’ states to\naccount for the statistical agreement.

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In this thesis, the article “Can a Future Choice Affect a Past Measurement’s\nOutcome?” is used as a starting point to explore the peculiar\ncorrelations between subsequent weak (i.e. non-projective) and\nstrong measurements in a variation of the EPR-Bell experiment. Bell’s\ntheorem states that particles may not possess predetermined values.\nHowever, as the outcomes of the subsequent weak and strong measurements\ndo statistically agree, an apparent contridiction arises. The\nauthors claim that the correlations between the results are best explained\nusing the time-symmetric two-state vector formalism, stating\nthat the experimenter’s future choice has been encrypted in the weak\nmeasurement’s outcomes.\nAlternative explanations are analyzed and a numerical simulation was\nmade to invigorate the notion of a so called weak-bias. Meaning that\nthe weak measurements sufficiently influence the particles’ states to\naccount for the statistical agreement.
An EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations, whose outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these measurements and the earlier weak ones within the pair. A contradiction thereby ensues: i) Bell's theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement's outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
Quantum weak measurement is presented as shedding new light on the retrocausality question. It is shown to leave a system almost unaffected while gathering information about it. Next, an EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations. These weak outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction thereby ensues: i) Bell’s theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones, suggesting the existence of pre-determined values. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement’s outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner (Found Phys 47:697-707, 2017), Kastner seems to take us many years backwards in the the debate, casting doubt on the very term "weak value" and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. (Ann Phys 355:258-268, 2015) in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology (which is indeed interpretational and far more complex than that described by Kastner) and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by (strong) projective measurements, without the need of employing weak measurements.
The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be abstract properties of systems describing a complete picture between successive measurements in the two-state vector formalism (TSVF). The remarkable achievements of the weak value formalism in experimental quantum mechanics have persuaded most quantum physicists that it is impeccable. However, we explore a scenario where the formalism of weak values for mixed states is employed in a quantum communication protocol, but discover that it generates inaccurate outcomes. This reinforces our previous conclusion that the weak values may not be elements of the reality of weak measurements, contrary to what the proponents of weak values proposed.