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arXiv:2203.00254 · Physical Review A

Isolating noise and amplifying the signal using weak quantum measurement and postselection

Ahana Ghoshal, Soham Sau, Debmalya Das, Ujjwal Sen

Published May 22, 2023• 8 citations
arXivHTMLPDF

Abstract

The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a ``cat'', is dissociated from a property of the object, identified with the ``grin'' of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g., two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit-coupling--like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a so-called confused Cheshire cat. We devise a gedanken experiment in which such a ``confusion'' can be successfully dissociated from the system, and we find that the dissociation helps in the amplification of signals.

DOI
10.1103/physreva.107.052214

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The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a cat'', is dissociated from a property of the object, identified with the grin'' of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g., two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit-coupling--like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a so-called confused Cheshire cat. We devise a gedanken experiment in which such a ``confusion'' can be successfully dissociated from the system, and we find that the dissociation helps in the amplification of signals.
The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.
We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.
Abstract A common-sense perception of a physical system is that it is inseparable from its physical properties. The notion of quantum Cheshire cat challenges this, as far as quantum systems are concerned. It shows that a quantum system can be decoupled from its physical property under suitable pre and postselections. However, in the quantum Cheshire cat setup, the decoupling is not permanent. The photon, for example, and its circular polarization is separated and then recombined. In this paper, we present a thought experiment where we decouple two photons from their respective polarizations and then interchange them during recombination. Thus, our proposal shows that that the belongingness of a property for a physical system is very volatile in the quantum world. This raises the question of reality of an observable at a much deeper level.
Based on the concept of weak measurements, in 2013 Aharonov et al. proposed an experiment in which, according to their interpretation of the predicted results, a photon and its circular polarization were spatially separated, naming this phenomenon quantum Cheshire Cat [1]. This name is after a character in Lewis Carrolls novel Alice In Wonderland, the Cheshire Cat a cat whose grin can exist without the animal itself. Denkmayr et al., in 2014, claimed they realized experimentally the quantum Cheshire Cat, separating a neutron from its intrinsic magnetic moment [3]. We show how both results follow from interference effects, and thus the conclusion that a particle is separated from one of its intrinsic properties is not a necessary one. Making use of mostly undergraduate level quantum mechanics, we rule out the apparent paradox of the quantum Cheshire Cat.
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.
In Alice's Adventures in Wonderland by Lewis Carroll, mischievous grin of a Cheshire cat is sometimes dis-embodied from her body. Quantum theory allows such a counterintuitive phenomenon, known as the quantum Cheshire cat effect [1], to happen for a pre- and post-selected (PPS) system. While observing the quantum Cheshire cat, the physical property and the carrier's location should be weakly probed with a measuring device to leave the quantum state with negligible disturbance. To date, experimental observations of the quantum Cheshire cat effect have been realized with a single neutron as well as with a single photon [2, 3]. However, their observations relied on weakly disturbing elements instead of a true weak measuring device. In this work, we report the experimental observation of the quantum Cheshire cat effect with a weak measuring device. To investigate the quantum Cheshire cat effect, we employ a photon pair generated by spontaneous parametric down conversion (SPDC). The elements of quantum Cheshire cat, namely the body (photon) and the grin (polarization), are indirectly probed with a quantum pointer using another single photon, where both the body and the grin are weakly measured without destroying the photon itself.