Preparation of arbitrary quantum states with regular 
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 functions

Kuhn, Barbara; Vogel, W.

doi:10.1103/physreva.98.053807

Cited by 6 publications

(8 citation statements)

References 64 publications

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“…Which of the two solutions is realized depends on the initial conditions. For other parameter values we have also observed solutions that switch between periods of upward and downward motion [33].…”

Section: Numerical Integration Of the Time-dependent Problemsupporting

confidence: 55%

“…Under certain conditions the symmetry of the direction of motion with respect to the field and anisotropy direction appears to be spontaneously broken, i.e. we have observed stationary island migration off the field direction even when the latter coincides with a symmetry axis of the anisotropy [33]. This behavior may be related to the discontinuity of the direction of motion when the field direction crosses the direction of minimal mobility, which was described in Sect.3.2 for the capillarity-free case.…”

Section: Numerical Integration Of the Time-dependent Problemmentioning

confidence: 85%

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Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

Kühn

Krug

Multiscale Modeling in Epitaxial Growth

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We consider the shape evolution of two-dimensional islands on a crystal surface in the regime where mass transport is exclusively along the island edge. A directed mass current due to surface electromigration causes the island to migrate in the direction of the force. Stationary shapes in the presence of an anisotropic edge mobility can be computed analytically when the capillary effects of the line tension of the island edge are neglected, and conditions for the existence of non-singular stationary shapes can be formulated. In particular, we analyse the dependence of the direction of island migration on the relative orientation of the electric field to the crystal anisotropy, and we show that no stationary shapes exist when the number of symmetry axes is odd. The full problem including line tension is solved by time-dependent numerical integration of the sharp-interface model. In addition to stationary shapes and shape instability leading to island breakup, we also find a regime where the shape displays periodic oscillations. (2000). Primary 53C44; Secondary 82C24. Mathematics Subject Classification

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Section: Numerical Integration Of the Time-dependent Problemsupporting

confidence: 55%

Section: Numerical Integration Of the Time-dependent Problemmentioning

confidence: 85%

Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

Kühn

Krug

Multiscale Modeling in Epitaxial Growth

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“…Therefore, in this sense, the filtered state ρ Ω is a noisy version of the original state ρ. In practice, to implement a displacement operation on a quantum state, one can overlap the state on a highly transmissive beamsplitter with a coherent state [33].…”

Section: Necessary and Sufficient Condition For Physicality Of A Filt...mentioning

confidence: 99%

“…where 0 ≤ L ≤ ∞ is the width parameter such that lim L→∞ Ω L (ξ) = Ω L (0) = 1. Therefore, the Fourier transform of the filter function ΩL (ξ) is always guaranteed to be a probability density, and the negativity in the regularized GSP, P Ω (α), which is the GSP of ρ Ω [33], indicates the nonclassicality of the state ρ.…”

Section: B Nonclassicality Filtersmentioning

confidence: 99%

Filter functions in quantum phase-space representations

Mani¹,

Shojaee²,

Rahimi-Keshari³

2022

Preprint

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Representation of quantum states in terms of phase-space quasiprobability distributions provides practical tools for identifying features such as the nonclassicality of quantum states. In this setting, filter functions are commonly used to regularize or smooth the phase-space quasiprobability distributions, in particular, the Glauber-Sudarshan P -function. We show that the quantum map associated with a filter function is completely positive and trace-preserving if and only if the Fourier transform of the filter function is a probability density distribution. In this case, filtering the quasiprobability distributions of a quantum state can be viewed as applying a random displacement operation on the quantum state according to the Fourier transform of the filter function. We derive a lower bound on the fidelity between the input and output states of a quantum filtering map. We illustrate several examples of filter functions corresponding to physical and nonphysical maps, in particular, a class of positive but not completely positive maps. We also discuss interesting applications of our results in estimating the output state of unknown quantum channels and estimating the outcome probabilities of quantum measurements.

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“…Nonclassical states of light find useful applications in tasks such as quantum metrology [1,2], quantum teleportation [3], quantum cryptography [4], quantum communication [5], and quantum information processing [6]. Correspondingly, there has been great interest in the characterization, verification, and quantification of nonclassicality in quantum states [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Due to the linearity of quantum mechanics, measurement statistics from a nonclassical state may be reproduced by a classical state by appropriately modifying the measurement [22].…”

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confidence: 99%

Negativity of Quasiprobability Distributions as a Measure of Nonclassicality

2020

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We demonstrate that the negative volume of any s-parametrized quasiprobability, including the Glauber-Sudashan P function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan P function, in particular, can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and we show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.

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Preparation of arbitrary quantum states with regular P functions

Cited by 6 publications

References 64 publications

Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

Filter functions in quantum phase-space representations

Negativity of Quasiprobability Distributions as a Measure of Nonclassicality

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