Abstract We analyse the quantum Cheshire cat using contextuality theory, to see if this can tell us anything about how best to interpret this paradox. We show that this scenario can be analysed using the relation between three different measurements, which seem to result in a logical contradiction. We discuss how this contextual behaviour links to weak values, and coherences between prohibited states. Rather than showing a property of the particle is disembodied, the quantum Cheshire cat instead demonstrates the effects of these coherences, which are typically found in pre- and post-selected systems.
Abstract We analyse the quantum Cheshire cat using contextuality theory, to see if this can tell us anything about how best to interpret this paradox. We show that this scenario can be analysed using the relation between three different measurements, which seem to result in a logical contradiction. We discuss how this contextual behaviour links to weak values, and coherences between prohibited states. Rather than showing a property of the particle is disembodied, the quantum Cheshire cat instead demonstrates the effects of these coherences, which are typically found in pre- and post-selected systems.
Abstract One of the common conceptions of nature, typically derived from the experiences with classical systems, is that attributes of the matter coexist with the substance. In the quantum regime, however, the quantum particle itself and its physical property may be in spatial separation, known as the quantum Cheshire cat effect. While there have been several reports to date on the observation of the quantum Cheshire cat effect, all such experiments are based on first-order interferometry and destructive projection measurement, thus allowing simple interpretation due to measurement-induced disturbance and also subject to trivial interpretation based on classical waves. In this work, we report an experimental observation of the quantum Cheshire cat effect with noninvasive weak quantum measurement as originally proposed. The use of the weak-measurement probe has allowed us to identify the location of the single photon and that of the disembodied polarization state in a quantum interferometer. The weak-measurement probe based on two-photon interference makes our observation unable to be explained by classical physics. We furthermore elucidate the quantum Cheshire cat effect as quantum interference of the transition amplitudes for the photon and the polarization state which are directly obtained from the measurement outcomes or the weak values. Our work not only reveals the true quantum nature of Cheshire cat effect but also sheds light on a comprehensive understanding for the counter-intuitive quantum phenomena.
Observing counterintuitive quantum phenomena have provided physical perspectives on quantum mechanics as well as important evidence of its validity. One of such phenomena, namely the quantum Cheshire cat effect, illustrates the situation that the physical property is disembodied from its physical carrier. Here, we experimentally demonstrate the quantum Cheshire cat effect with a nondestructive weak measuring device. A pre- and post-selected photonic quantum system is subject to a weak nondestructive measuring device to probe where the photon and its polarization property can be found. Intriguingly, a quantum pointer after the weak quantum measurement indicates that the polarization can be found at the path the photon did not take.
Observing counterintuitive quantum phenomena have provided physical perspectives on quantum mechanics as well as important evidence of its validity. One of such phenomena, namely the quantum Cheshire cat effect, illustrates the situation that the physical property is disembodied from its physical carrier. Here, we experimentally demonstrate the quantum Cheshire cat effect with a nondestructive weak measuring device. A pre- and post-selected photonic quantum system is subject to a weak nondestructive measuring device to probe where the photon and its polarization property can be found. Intriguingly, a quantum pointer after the weak quantum measurement indicates that the polarization can be found at the path the photon did not take.
Interest in weak values has grown steadily since their introduction in 1988, driven by developments in quantum measurement theory and increasing attention to the foundational issues at the heart of quantum mechanics. This thesis undertakes a philosophical investigation into the nature and implications of weak values, with a particular focus on their interpretation and role in creating and resolving quantum paradoxes. Overall, we argue that sequential weak values offer novel conceptual tools for assessing logical consistency in an atemporal fashion, ultimately motivating a shift toward a fundamentally relation-based ontology. Chapter 1 begins by establishing the conceptual and philosophical foundations of the thesis. We argue that performing this conceptual analysis of weak values requires a philosophical methodology informed by the structure of quantum theory and the foundational questions it poses. In Chapter 2, we provide a critical exploration of weak measurement theory and weak values, outlining their historical foundations and development, the experimental context, and interpretative challenges. Through a detailed analysis of paradoxes related to weak values such as the nested interferometer and the quantum Cheshire cat, the chapter argues that weak values reveal spatiotemporally discontinuous trajectories which conflict with classical intuition about particles and their trajectories. We contend that weak values are inherently contextual, as their significance arises in the context of the pre- and post- selections of the system. Chapter 3 develops an original account of ‘particle presence' across time, building on metaphysical notions of persistence. This chapter proposes a way of recovering continuity in paradoxes such as the three-box gendankenexperiment. Our framework offers a means of assessing the persistence of particles through spacetime via sequential weak values which we argue test the logical consistency of propositions across time. We then explore the implications for temporality, developing the key argument of this chapter: presence is defined across durations of time, rather than in discrete spacetime. This raises the possibility of presence without a well-defined causal order. In Chapter 4, the insights developed in the previous chapters are extended to a consideration of Relational Quantum Mechanics (RQM), addressing the longstanding issue of a lack of intersubjective agreement in relational interpretations. Given RQM's rejection of absolutism, this chapter critiques existing attempts at bridging perspectives and proposes a new route to empirical confirmation grounded in the persistence and reliability of observer's memory records. Our two- step model, consisting of internal confirmation via sequential weak values and then a consistency check from a second observer, offers a new approach to confirmation in RQM without rejecting the non-absolutist core of the interpretation. Sequential weak values are re-interpreted as atemporal probes available to the informational observer, distinct from its physical counterpart. This atemporal nature allows them to establish logical consistency across the observer's records and assign credence to them without presupposing a classical temporal order. These results suggest an ontology grounded in primitive relations, rather than one built on temporally ordered events. Chapter 4 thus builds on the contextuality arguments of earlier chapters: just as weak values reveal measurement outcomes to be context-dependent, their sequential and time-symmetric structure exposes temporal contextuality, challenging classical assumptions about fixed causal order and reinforcing the case for a non-classical, relation-based ontology. Finally, in Chapter 5, we conclude by summarising our key results and giving a list of open questions.
We analyze the quantum Cheshire cat dilemma under an entangled scenario based on atom-field interferometric setup that can be readily executed experimentally. Once the accuracy and the faithful workability of the two-state vector formalism along with the weak measurement theme is guaranteed, our analysis suggests that the interpretation, i.e., separation of a certain specific feature from the quantum entity, furnished in the pioneering Cheshire cat paper [Y. Aharonov, S. Popescu, D. Rohrlich, and P. Skrzypczyk, New J. Phys. 15, 113015 (2013)], cannot be taken for granted as the sole reason for the phenomenon. Rather, our analysis of the considered entangled interferometric scenario suggests an alternative point of view where the inaccessibility of the defining features of a quantum system appears to be a more plausible reason than the disembodying of the feature from the system itself. Our proposal is based on the time-tested tools of the atomic Bragg diffraction, operating in off-resonant regime, and utilizes the entangled correlations engineered between two identical, two-level atoms in the momentum space.