Directly estimating the Holevo capacity of discrete Weyl channels

Rehman, Junaid ur; Jeong, Youngmin; Shin, Hyundong

doi:10.1103/physreva.99.042312

Cited by 14 publications

(13 citation statements)

References 42 publications

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“…Furthermore, for any prime d, A d d+1 is sufficient. This latter observation is expected to hold beyond the values of d which we numerically checked, since it is not possible to construct a set of more than d + 1 noncommuting Weyl operators for a prime d [37]. Therefore, if A d d 2 −1 being sufficient for any d is always true, then the sufficiency of A d d+1 for any prime d also holds everywhere.…”

Section: Lemma 1 ([36]mentioning

confidence: 90%

“…2 Verbal description of our algorithm is as follows. We first utilize the results from [40] to calculate the total number of distinct eigenvalues of all discrete Weyl operators on H d . We make a set W d of all Weyl operators that have d distinct eigenvalues.…”

Section: Lemma 1 ([39]mentioning

confidence: 99%

“…We recall that γ = 0 in (17) gives completely depolarizing (highly noisy) channel, and γ = 1 gives an ideal (noiseless) DWC. Furthermore, increasing γ makes the channel parameters more ordered in terms of majorization, giving less noisy channels [40,46]. Also, we assume the unintended channel to be the depolarizing channel parameterized by a real parameter κ, where κ = 0, 1 corresponds to the noiseless and the fully depolarizing channels, respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Rehman

Shin

2021

Quantum

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We propose a parameter estimation protocol for generalized Pauli channels acting on d-dimensional Hilbert space. The salient features of the proposed method include product probe states and measurements, the number of measurement configurations linear in d, minimal post-processing, and the scaling of the mean square error comparable to that of the entanglement-based parameter estimation scheme for generalized Pauli channels. We also show that while measuring generalized Pauli operators the errors caused by the Pauli noise can be modeled as measurement errors. This makes it possible to utilize the measurement error mitigation framework to mitigate the errors caused by the generalized Pauli channels. We use this result to mitigate noise on the probe states and recover the scaling of the noiseless probes, except with a noise strength-dependent constant factor. This method of modeling Pauli channel as measurement noise can also be of independent interest in other NISQ tasks, e.g., state tomography problems, variational quantum algorithms, and other channel estimation problems where Pauli measurements have the central role.

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Section: Lemma 1 ([36]mentioning

confidence: 90%

Section: Lemma 1 ([39]mentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

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Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Rehman

Shin

2021

Quantum

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“…It was shown in Ref. [35,36] that the effect of a discrete Weyl channel (a generalization of Pauli qubit channels) on the eigenstates of a Weyl operator can be modeled as a classical symmetric channel. Since the state of interest ρ is diagonal in the eigenbasis of 𝑃, the same argument of modeling the Pauli channel as a classical symmetric channel holds here.…”

Section: Quantum Noisementioning

confidence: 99%

Error-mitigated photonic variational quantum eigensolver using a single-photon ququart

Lee¹,

Lee²,

Hong³

et al. 2021

Preprint

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We report the experimental resource-efficient implementation of the variational quantum eigensolver (VQE) using four-dimensional photonic quantum states of single-photons. The four-dimensional quantum states are implemented by utilizing polarization and path degrees of freedom of a single-photon. Our photonic VQE is equipped with the quantum error mitigation (QEM) protocol that efficiently reduces the effects of Pauli noise in the quantum processing unit. We apply our photonic VQE to estimate the ground state energy of He-H + cation. The simulation and experimental results demonstrate that our resource-efficient photonic VQE can accurately estimate the bond dissociation curve, even in the presence of large noise in the quantum processing unit.

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“…Recently, there has been significant interest in calculating the classical capacity of quantum channels. Rehman et al used the majorization procedure to provide lower and upper estimations of the Holevo capacity of the Weyl channels [21,22]. Amosov calculated the classical capacity for deformations of classical-quantum Weyl channels [23] and channels generated by irreducible projective unitary representations of finite groups [24].…”

Section: Introductionmentioning

confidence: 99%

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

Siudzińska

Das

Bera

2021

Entropy

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In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.

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Directly estimating the Holevo capacity of discrete Weyl channels

Cited by 14 publications

References 42 publications

Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Error-mitigated photonic variational quantum eigensolver using a single-photon ququart

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

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