Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size

You, Jun-Kai; Cheng, Hao-Chung; Li, Yen-Huan

doi:10.48550/arxiv.2109.06054

Cited by 2 publications

(2 citation statements)

References 49 publications

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“…We remark that several entropic quantities such as H * α and I * α do not have closed-form expressions for α = 1 in general. There is a recent optimization algorithm with asymptotic convergence guarantee that can be applied to compute them [38]. It is intriguing to note that some entropic exponent functions obtained in this paper such as H ↓ α and I ↓ α have the same form as classical-quantum channel coding [33,36] and classical data compression with quantum side information [32].…”

Section: Discussionmentioning

confidence: 83%

Strong Converse for Privacy Amplification against Quantum Side Information

Shen¹,

Li²,

Cheng³

2022

Preprint

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We establish a one-shot strong converse bound for privacy amplification against quantum side information using trace distance as a security criterion. This strong converse bound implies that in the independent and identical scenario, the trace distance exponentially converges to one in every finite blocklength when the rate of the extracted randomness exceeds the quantum conditional entropy. The established one-shot bound has an application to bounding the information leakage of classical-quantum wiretap channel coding and private communication over quantum channels. That is, the trace distance between Alice and Eavesdropper's joint state and its decoupled state vanishes as the rate of randomness used in hashing exceeds the quantum mutual information. On the other hand, the trace distance converges to one when the rate is below the quantum mutual information, resulting in an exponential strong converse. Our result also leads to an exponential strong converse for entropy accumulation, which complements a recent result by Dupuis [arXiv:2105.05342]. Lastly, our result and its applications apply to the moderate deviation regime. Namely, we characterize the asymptotic behaviors of the trace distances when the associated rates approach the fundamental thresholds with speeds slower than O( 1 / √ n).

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Section: Discussionmentioning

confidence: 83%

Strong Converse for Privacy Amplification against Quantum Side Information

Shen¹,

Li²,

Cheng³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We remark that both the quantities introduced in (2.1) and (2.2) do not have a closed-form expression. However, an iterative optimization algorithm with convergence guarantees has been proposed to compute them [26].…”

Section: Notation and Information Quantitiesmentioning

confidence: 99%

Error Exponent and Strong Converse for Quantum Soft Covering

Cheng¹,

Li²

2022

Preprint

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How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem. Namely, we use a random codebook with codewords independently sampled from a prior distribution and send it through a classical-quantum channel to approximate the target state. When using a random independent and identically distributed codebook with a rate above the quantum mutual information, we show that the expected trace distance between the codebook-induced state and the target state decays with exponent given by the sandwiched Rényi information. On the other hand, when the rate of the codebook size is below the quantum mutual information, the trace distance converges to one exponentially fast. We obtain similar results when using a random constant composition codebook, whereas the sandwiched Augustin information expresses the error exponent. In addition to the above large deviation analysis, our results also hold in the moderate deviation regime. That is, we show that even when the rate of the codebook size approaches the quantum mutual information moderately quickly, the trace distance still vanishes asymptotically.

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Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size

Cited by 2 publications

References 49 publications

Strong Converse for Privacy Amplification against Quantum Side Information

Strong Converse for Privacy Amplification against Quantum Side Information

Error Exponent and Strong Converse for Quantum Soft Covering

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