Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels

by   Touheed Anwar Atif, et al.

We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan, arXiv:2302.00625]. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author.


page 1

page 2

page 3

page 4


Optimizing the fundamental limits for quantum and private communication

The quantum capacity of a noisy quantum channel determines the maximal r...

One-shot inner bounds for sending private classical information over a quantum MAC

We provide the first inner bounds for sending private classical informat...

One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information

We study the communication capabilities of a quantum channel under the m...

Lossy Quantum Source Coding with a Global Error Criterion based on a Posterior Reference Map

We consider the lossy quantum source coding problem where the task is to...

A Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels

Achievability in information theory refers to demonstrating a coding str...

Almost exact analysis of soft covering lemma via large deviation

This paper investigates the soft covering lemma under both the relative ...

One shot approach to lossy source coding under average distortion constraints

This paper present a one shot analysis of the lossy compression problem ...

Please sign up or login with your details

Forgot password? Click here to reset