Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Rehman, Junaid ur; Shin, Hyundong

doi:10.22331/q-2021-07-01-490

Cited by 16 publications

(6 citation statements)

References 56 publications

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“…A noiseless measurement device corresponds to λ = 0, and a completely random measurement device has λ = 1. This particular measurement can also be modeled as a depolarizing noise on the state before measurement, followed by a noiseless measurement device [32].…”

Section: Resultsmentioning

confidence: 99%

Self-Guided Quantum State Learning for Mixed States

Farooq¹,

Ullah²,

Ramadhani³

et al. 2021

Preprint

Self Cite

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We provide an adaptive learning algorithm for tomography of general quantum states. Our proposal is based on the simultaneous perturbation stochastic approximation algorithm and is applicable on mixed qudit states. The salient features of our algorithm are efficient (O d 3 ) post-processing in the dimension d of the state, robustness against measurement and channel noise, and improved infidelity performance as compared to the contemporary adaptive state learning algorithms. A higher resilience against measurement noise makes our algorithm suitable for noisy intermediate-scale quantum applications.

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Section: Resultsmentioning

confidence: 99%

Self-Guided Quantum State Learning for Mixed States

Farooq¹,

Ullah²,

Ramadhani³

et al. 2021

Preprint

Self Cite

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“…This provides us with a unique situation, where we can correct the final state through a reversal unitary operator U † p based on the probability p of bit-flip noise. For identifying this parameter p, channel/process tomography techniques can be employed [42]. This is unlike the case of general quantum communication, where mixedness (decrease in purity) cannot be removed without using and sacrificing copies of the output states via purification [31].…”

Section: ) Bit-flip Noisementioning

confidence: 99%

Noise-Robust Quantum Teleportation With Counterfactual Communication

2022

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Direct counterfactual communication (DCC) based on the dynamic quantum Cheshire cat effect is an interesting protocol for particle-less information transfer. In this paper, we propose a noise-robust, completely counterfactual, teleportation scheme based on the modified DCC. We show that our scheme does not require any a priori shared phase reference; an essential requirement for conventional teleportation schemes. For our modified DCC, we investigate the noise acting on the remotely controlled properties of a photon, i.e., path and polarization. We show that our proposed modification and resulting teleportation scheme are robust against channel delay and dephasing noise. While for photonic loss, depolarizing, and bit-flip noise, it is possible to obtain the correct state given only the channel state information.

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“…There are several prior works that study the estimation of so-called generalized Pauli channels, which act on a d-dimensional quantum system and do not contain explicit tensor product structure. These works typically (though not always [27]) make the much stronger assumption that ideal entangled states can be prepared to assist the channel estimation, and they focus on finding efficient estimators that saturate the Cramér-Rao bound. Fujiwara and Imai first showed that entanglement-assisted channel estimation of generalized Pauli channels could achieve the Cramér-Rao bound [12], though much simpler proofs of such theorems are now available [16,].…”

Section: Previous and Related Workmentioning

confidence: 99%

Pauli error estimation via Population Recovery

Flammia

O’Donnell

2021

Quantum

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Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ϵ in ℓ∞ using just O(1/ϵ2)log⁡(n/ϵ) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ϵ) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤1/4.We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1−η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1±ϵ (i.e., additive precision ϵη) using just O(1ϵ2η)log⁡(n/ϵ) applications of the channel.

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Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Cited by 16 publications

References 56 publications

Self-Guided Quantum State Learning for Mixed States

Self-Guided Quantum State Learning for Mixed States

Noise-Robust Quantum Teleportation With Counterfactual Communication

Pauli error estimation via Population Recovery

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