Wigner negativity in spin-
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 systems

Davis, Jack L.; Kumari, Meenu; Mann, Robert B.; Ghose, Shohini

doi:10.1103/physrevresearch.3.033134

Cited by 17 publications

(10 citation statements)

References 43 publications

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“…Fortunately, the Wigner function can be viewed as a quantum analogy to the classical probability density, which is able to visualize the evolution of the walker in the phase space. Following the Stratonovich-Weyl correspondence [40,42,43], the Wigner function for the SU(2) group can be defined as…”

Section: Resultsmentioning

confidence: 99%

“…which have two terms. Each term is composed of a superposition of two spin coherent states, that can be regarded as the spin cat state [40,41]. The probability distribution for the non-orthogonal (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…It has been widely employed to study the cooperative phenomena [34], such as the superradiant phase transition, quantum magnetism and so on. In addition, the spin coherent state is an essential ingredient to construct the spin cat state and spin compass state [40,41].Like the bosonic coherent state, the spin coherent states are also non-orthogonal and can be generated in the experiments [33,35]. A visual description to the walker's states on the Bloch sphere can be achieved by calculating the Wigner function [40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Quantum walk on the Bloch sphere

Duan

2022

Preprint

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A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, while its location on the Bloch sphere is described by the spin coherent state. An additional spin that interacts with the spin cluster plays the role of a coin, whose state determines the rotation of the spin cluster. The Wigner function is calculated to visualize the movement of the walker on the Bloch sphere, with which the probability distribution and the standard deviation are also achieved. The quadratic enhancement of variance for the quantum walk on the Bloch sphere is confirmed. Compared to the ideal quantum walk on a circle, the walker's states on the Bloch sphere are non-orthogonal, whose drawbacks can be eliminated by increasing the number of spins in the spin cluster.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum walk on the Bloch sphere

Duan

2022

Preprint

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“…Last but not least, some of these results will change for higher spin systems, e.g., when we take the detector to be the spin-j representation of SU (2) instead of spin-1/2 system. To illustrate one such difference, note that for qubits (j = 1/2) the SU (2)-covariant Wigner negativity is known to be completely specified by its purity and hence the Bloch length, while for j ≥ 1 this is no longer the case [99,100]. Hence, even for classification of non-classicality, higher-spin systems no longer share the same property.…”

Section: Discussionmentioning

confidence: 99%

Characterization of non-perturbative qubit channel induced by a quantum field

Tjoa¹

2022

Preprint

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In this work we provide some characterization of the quantum channel induced by nonperturbative interaction between a single qubit with a quantized massless scalar field in arbitrary globally hyperbolic curved spacetimes. The qubit interacts with the field via Unruh-DeWitt detector model and we consider two non-perturbative regimes: (i) when the interaction is very rapid, effectively at a single instant in time (delta-coupled detector); and (ii) when the qubit has degenerate energy level (gapless detector). We organize the results in terms of quantum channels and Weyl algebras of observables in the algebraic quantum field theory (AQFT). We collect various quantum information-theoretic results pertaining to these channels, such as entropy production of the field and the qubit, recoverability of the qubit channels, and causal propagation of noise due to the interactions. We show that by treating the displacement and squeezing operations as elements of the Weyl algebra, we can generalize existing non-perturbative calculations involving the qubit channels to non-quasifree Gaussian states in curved spacetimes with little extra effort and provide transparent interpretation of these unitaries in real space. We also generalize the existing result about cohering and decohering power of a quantum channel induced by the quantum field to curved spacetimes in a very compact manner.

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“…Since all pure qubit states are trivially spin coherent states connected through rigid rotations, they all have the same Wigner negativity. This has been calculated to be 1 2 − 1 √ 3 ≈ 0.077 [52,53].…”

Section: Small Spinsmentioning

confidence: 99%

Stellar representation of extremal Wigner-negative spin states

Davis¹,

Hennigar²,

Mann³

et al. 2022

Preprint

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The Majorana stellar representation is used to characterize spin states that have a maximally negative Wigner quasiprobability distribution on a spherical phase space. These maximally Wigner-negative spin states generally exhibit a partial but not high degree of symmetry within their star configurations. In particular, for spin j > 2, maximal constellations do not correspond to a Platonic solid when available and do not follow an obvious geometric pattern as dimension increases. In addition, they are generally different from spin states that maximize other measures of nonclassicality such as anticoherence or geometric entanglement.Random states (j ≤ 6) display on average a relatively high amount of negativity, but the extremal states and those with similar negativity are statistically rare in Hilbert space. We also prove that all spin coherent states of arbitrary dimension have non-zero Wigner negativity. This offers evidence that all pure spin states also have non-zero Wigner negativity. The results can be applied to qubit ensembles exhibiting permutation invariance.

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Wigner negativity in spin- j systems

Cited by 17 publications

References 43 publications

Quantum walk on the Bloch sphere

Quantum walk on the Bloch sphere

Characterization of non-perturbative qubit channel induced by a quantum field

Stellar representation of extremal Wigner-negative spin states

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