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Is the dynamical quantum Cheshire cat detectable?

Jonte R. Hance, J Ladyman, JG Rarity

Published Jul 17, 2024• 0 citations
Publisher

Abstract

We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al. We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude ('field') of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is |↑z〉, we need to bias this with some small amount δ of state |↓z〉). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ. We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.

DOI
10.25405/ncl.34502412

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Is the dynamical quantum Cheshire cat detectable?

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Abstract We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude (‘field’) of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is | ↑ z ⟩ , we need to bias this with some small amount δ of state | ↓ z ⟩ ). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ. We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.

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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.

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Hunting for the Quantum Cheshire Cat

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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.

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We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al. We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude ('field') of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is |↑z〉, we need to bias this with some small amount δ of state |↓z〉). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ. We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.
Abstract We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude (‘field’) of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is | ↑ z ⟩ , we need to bias this with some small amount δ of state | ↓ z ⟩ ). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ. We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.
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.
Here we report a type of dynamic effect that is at the core of the so called "counterfactual computation" and especially "counterfactual communication" quantum effects that have generated a lot of interest recently. The basic feature of these counterfactual setups is the fact that particles seem to be affected by actions that take place in locations where they never (more precisely, only with infinitesimally small probability) enter. Specifically, the communication/computation takes place without the quantum particles that are supposed to be the information carriers travelling through the communication channel or entering the logic gates of the computer. Here we show that something far more subtle is taking place: It is not necessary for the particle to enter the region where the controlling action takes place; it is enough for the controlled property of the particle, (i.e., the property that is being controlled by actions in the control region), to enter that region. The presence of the controlled property, without the particle itself, is possible via a quantum Cheshire Cat type effect in which a property can be disembodied from the particle that possesses it. At the same time, we generalize the quantum Cheshire Cat effect to dynamical settings, in which the property that is "disembodied" from the particle possessing it propagates in space, and leads to a flux of "disembodied" conserved quantities.
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.
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.