Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

Cormann, Mirko; Caudano, Yves

doi:10.1088/1751-8121/aa7639

Cited by 18 publications

(17 citation statements)

References 60 publications

(131 reference statements)

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“…Although the current work discusses weak values in relation to signal amplification, it may be worthwhile to mention a few other applications of the idea. Weak values can be used in the direct measurement of a photon wavefunction [14,16], to measure the spin Hall effect [13], in quantum state tomography [17,18], in the geometric description of quantum states [19] and state visualization [20]. It also finds application in quantum thermometry [21], and measuring the expectation value of non-Hermitian operators [22,23].…”

Section: Introductionmentioning

confidence: 99%

Isolating noise and amplifying signal with quantum Cheshire cat

Soham¹,

Ghoshal²,

Das³

et al. 2022

Preprint

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The 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 "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 amplification of signals.

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Section: Introductionmentioning

confidence: 99%

Isolating noise and amplifying signal with quantum Cheshire cat

Soham¹,

Ghoshal²,

Das³

et al. 2022

Preprint

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“…[5][6][7][8][9][10][11][12]. While there has been a great deal of debates and discussions on the meaning and interpretation of weak value and on the implications it can have on the foundations of quantum mechanics [3,13,14], the concept has found myriad applications, including signal amplification [15], spin Hall effect [6], quantum state tomography [16,17], geometric description of quantum states [18], state visualization [19], directly measuring the wave function of a photon [7,20], measuring the expectation value of non-Hermitian operators [21,22], and quantum thermometry [23]. Weak values have also led to unearthing the possibilities of a number of counter-intuitive results such as the Hardy's paradox [24] and the three-box paradox [3].…”

Section: Introductionmentioning

confidence: 99%

Delayed choice of paths selected by grin and snarl of quantum Cheshire Cat

Das,

Sen

2020

Preprint

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The quantum Cheshire Cat is a mysterious phenomenon that temporarily strips a system -a "cat" -of its property -its "grin". A corollary of this effect is the decoupling of two properties of the same system, which we call the grin and the snarl. This can in principle be realized by detecting two components of polarization of a photon in two different arms of an interferometer. We introduce a mechanism by which we can interchange the positions of these two properties. By doing this we uncover a phenomenon that decouples the grin and the snarl, and puts them in their place even before they encounter the mechanism.

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“…Modular Values were introduced as an explanation of an experiment demonstrating the Hardy paradox [30,31], which involved the Weak Value of a product, and as a method to obtain Weak Values using strong measurement. Later on it extended theoretically in several ways [32] and also implemented experimentally [33].…”

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confidence: 99%

Direct Measurement of a Nonlocal Entangled Quantum State

Pan

Kedem

et al. 2019

Phys. Rev. Lett.

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Entanglement and wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using Weak Values, was demonstrated by Lundeen et al., Nature 474, 188(2011). However it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining Weak Values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using Modular Values. The method is experimentally implemented for a photon pair in a hyper-entangled state, i.e. entangled both in polarization and momentum degrees of freedom.

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Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

Cited by 18 publications

References 60 publications

Isolating noise and amplifying signal with quantum Cheshire cat

Isolating noise and amplifying signal with quantum Cheshire cat

Delayed choice of paths selected by grin and snarl of quantum Cheshire Cat

Direct Measurement of a Nonlocal Entangled Quantum State

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