Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy’s Paradox

Abstract

It has been proposed that the ability to perform joint weak measurements on post-selected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here, we experimentally perform weak measurements of joint (i.e. nonlocal) observables. In an implementation of Hardy's Paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the Paradox. Remarkably, the resulting weak probabilities verify all these statements but, at the same time, resolve the Paradox.Retrodiction is a controversial topic in quantum mechanics [1]. How much is one allowed to say about the history (e.g. particle trajectories) of a post-selected ensemble? Historically this has been deemed a question more suitable for philosophy (e.g. counterfactual logic) than physics; since the early days of quantum mechanics, the standard approach has been to restrict the basis of our physical interpretations to direct experimental observations. On the practical side of the question, postselection has recently grown in importance as a tool in fields such as quantum information: e.g. in linear optics quantum computation (LOQC) [2], where it drives the logic of quantum gates; and in continuous variable systems, for entanglement distillation [3]. Weak measurement is a relatively new experimental technique for tackling just this question. It is of particular interest to carry out weak measurements of multi-particle observables, such as those used in quantum information. Here, we present an experiment that uses weak measurement to examine the two-particle retrodiction paradox of Hardy [4,5], confirming the validity of certain retrodictions and identifying the source of the apparent contradiction.Hardy's Paradox is a contradiction between classical reasoning and the outcome of standard measurements on an electron E and positron P in a pair of MachZehnder interferometers (see Fig. 1). Each interferometer is first aligned so that the incoming particle always leaves through the same exit port, termed the "bright" port B (the other is the "dark" port D). The interferometers are then arranged so that one arm (the "Inner" arm I) from each interferometer overlaps at Y. It is assumed that if the electron and positron simultaneously enter this arm they will collide and annihilate with 100% probability. This makes the interferometers "InteractionFree Measurements" (IFM) [6]: that is, a click at the dark port indicates the interference was disturbed by an object located in one of the interferometer arms, without the interfering particle itself having traversed that arm. Therefore, in Hardy's Paradox a click at the dark port of the electron (positron) indicates that the positron (electron) was in the Inner arm. Consider if one were to detect both particles at the dark ports. As IFMs, these results would indicate the particles were simultaneously in the Inner arms and, therefore should have annihilated. But this is in contradi...

Advantages of nonclassical pointer states in postselected weak measurements

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Honoring Epimenides of Crete (±Δx): From Quantum Paradoxes, through Weak Measurements, to the Nature of Time

“…2.4) and negative weak values of projection operators (Sec. 3.4) are presented in [32]. Furthermore, as we concluded in [10], weak measurements (or more specifically, protective measurements [33]) can be used to track the wavefunction's changes after each partial measurement introduced in Sec.…”

A Pointer Theory Explanation of Weak Value Persistence Occurring in the Quantum Three Box Experimental Data

“…[7,8], as well as in the theoretical and experimental resolution of "Hardy's paradox", e.g. [9,10], and the "quantum box problem", e.g. [11,12].…”