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Physical Review A

Entanglement and the paradox of untying the defining feature from a quantum entity

Rameez‐ul‐Islam, Manzoor Ikram, Muhammad Imran, Guo-Qin Ge

Published Nov 27, 2019• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.100.052122

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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.
The phenomenon of the quantum Cheshire cat (QCC) and its interpretation by Aharanov et al. [ New J. Phys. 15 , 113015 ( 2013 ) NJOPFM 1367-2630 10.1088/1367-2630/15/11/113015 ], with the conjecture that any quantum entity can be disembodied from its physical attributes, has resulted in a heated debate leading to interpretational controversy as well as practical consequences. Here, we propose an experimentally testable and physically more realistic and logically plausible interpretation. We utilize a specifically engineered Mach–Zehnder-type interferometeric setup that is quite similar to the original QCC setup but with the slight difference that now a single-photon, bipartite entangled state traverses the interferometer such that each path is designated to a photon with different tags. With this specific setup, we demonstrate that the photon’s polarization is never physically separated from the photon itself. Rather, it becomes dormant and hence inaccessible along the designated interferometric path. We also generalize the schematics and show that any precisely oriented photon’s polarization that stands inaccessible or dormant re-emerges along the same spatially separated and isolated arm as we tune the polarization vector away from the selected angle. Thus our proposal persuasively proves that polarization is never stripped off the photon itself and instead becomes inaccessible along the interferometeric arm for a certain particularly selected orientation. The schematics further reveal that this inaccessibility of the photon’s polarization is not permanent, fixed, and universal, but rather it is entirely constrained to a specific orientation in the Hilbert space, governed by the particular pre- and post-selected state under two-state vector formalism.
Abstract We suggest an idea to implement the Cheshire Cat in atomic media. The proposal is based on the time-tested tools of the Bragg regime atom interferometry and can be easily executed under the prevailing cavity quantum electrodynamics (QED) research environment. Our analysis, based on weak measurements, clearly demonstrates that under certain specific pre- and post-selected scenarios, the atom strangely behaves as being in one arm of the interferometer whereas the signatures of its energy levels exist in the other arm simultaneously.
We analyze the proposal of Aharonov, Popescu, Rohrlich and Skrzypczyk [New. J. Phys. 15, 113015] of disembodying physical properties from particles. We argue that a different criterion, based on the cross-average $\langle \mathrm{`}cat\ somewhere \mbox{'}\times \mathrm{`}grin\ somewhere\ else\mbox{'}\rangle$ should be used to detect the disembodiment, rather than the local averages $\langle \mathrm{`}cat\ somewhere \mbox{'}\rangle$ and $\langle\mathrm{`}grin\ somewhere\ else\mbox{'}\rangle$. Here, the exact probability distribution and its characteristic function are derived for arbitrary coupling strength, preparation and post-selection. This allows to successfully hunt down the quantum Cheshire cat, showing that it is a consequence of interference, that it is present also for intermediate-strength measurements, and that it is a rather common occurrence in post-selected measurements.
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.
In a recent work, Aharonov et al suggested that a photon could be separated from its polarization in an experiment involving pre- and post-selection (Aharonov et al 2013 New J. Phys. 15 113015 ). They named the effect 'quantum Cheshire Cat', in a reference to the cat that is separated from its grin in the novel Alice ' s Adventures in Wonderland . Following these ideas, Denkmayr et al performed a neutron interferometric experiment and interpreted the results suggesting that neutrons were separated from their spin (Denkmayr et al 2014 Nat. Commun. 5 4492 ). Here we show that these results can be interpreted as simple quantum interference, with no separation between the quantum particle and its internal degree of freedom. We thus hope to clarify the phenomenon with this work, by removing these apparent paradoxes.