Quantum Information Theory | Kun WANG

Researchers make progress on quantum dense coding with locality constraints on decoder

Mon, 17 Oct 2022 00:00:00 +0000

The research achievement has been reported on the official website of and .

Dense coding is one of the earliest and most prominent quantum protocols that reveal the power of quantum entanglement in communication. Although it has been intensively studied, it has typically been restricted to scenarios where the receiver can perform global measurements to decode information, which is experimentally challenging. Thus, it is natural to impose locality conditions on the decoders from a practical perspective.

A research group led by Chief Research Scientist Masahito Hayashi of the Shenzhen Institute for Quantum Science and Engineering (SIQSE) at the Southern University of Science and Technology (SUSTech) has recently made progress on the study of quantum dense coding. In their study, they consider the dense coding scenario where certain asymmetry and locality constraints are imposed on the encoder and decoder.

Their paper, entitled “Dense Coding with Locality Restriction on Decoders: Quantum Encoders versus Superquantum Encoders,” was published in PRX Quantum, a well-recognized physics journal.

In this work, the researchers explored the practicality of dense coding by elaborating 21 classes of dense coding capacities with different encoder-decoder pairs, where the encoders are constrained by the resource theory of asymmetry and the decoders are constrained by various locality conditions.

Their contributions were to firstly show that all these capacities are equal and derive a single-letter capacity formula; secondly, prove that all these capacities satisfy the desirable strong converse property; and thirdly, establish an equivalence among three different quantities of a bipartite quantum state – the operationally defined dense coding capacity, the mathematically defined regularized asymmetry of assistance, and the quantum entropy of the twirled quantum state – thus providing the regularized asymmetry of the assistance measure an operational meaning.

The results of this work significantly push forward the research of practical dense coding in both the one-shot and asymptotic regimes within different resource theories. These results deepen our understanding of quantum entanglement and dense coding, and, more generally, classical and quantum communication via quantum resources.

Masahito Hayashi is the first author of this paper. He is also a fellow of the Institute of Electrical and Electronics Engineers (IEEE), Asia-Pacific Artificial Intelligence Association (AAIA), and Institute of Mathematical Statistics (IMS). The corresponding authors are Masahito Hayashi and Kun Wang, who is a former postdoctoral researcher in Hayashi’s group. The first affiliation of the paper is SIQSE.

The research was supported by the National Natural Science Foundation of China (NSFC), Guangdong Provincial Key Laboratory, Science, Technology and Innovation Commission of Shenzhen Municipality, and SUSTech.

Paper link:

Dense Coding with Locality Restriction on Decoders: Quantum Encoders versus Superquantum Encoders

Thu, 29 Sep 2022 00:00:00 +0000

Brief Summary

In this work, we explore the practicality of dense coding by elaborating 21 classes of dense coding capacities with different encoder-decoder pairs, where the encoders are constrained by the resource theory of asymmetry and the decoders are constrained by various locality conditions. Our contributions are to 1) show that all these capacities are equal and derive a single-letter capacity formula; 2) prove that all these capacities satisfy the desirable strong converse property; and 3) establish an equivalence among three different quantities of a bipartite quantum state—the operationally defined dense coding capacity, the mathematically defined regularized asymmetry of assistance, and the quantum entropy of the twirled quantum state—thus providing the regularized asymmetry of the assistance measure an operational meaning.

Our results significantly push forward the research of practical dense coding in both the one-shot and asymptotic regimes within different resource theories. These results deepen our understanding of quantum entanglement and dense coding, and, more generally, the classical and quantum communication via quantum resources.

Published in .

Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction

Thu, 04 Mar 2021 00:00:00 +0000

Permutation Enhances Classical Communication Assisted by Entangled States

Fri, 19 Feb 2021 00:00:00 +0000

Abstract

We study classical communication over a noisy quantum channel when bipartite states are preshared between the sender and the receiver, and one of the following encoding strategies are available: i) local operations; ii) local operations and one-way classical communication; iii) local operations and global permutations. Our main result is a capacity formula for strategy iii). This formula's two endpoints are the capacity formula in strategy i) and the entanglement-assisted classical capacity. Interestingly, these capacities satisfy the strong converse property, and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. We prove that the difference between the capacities by strategy i) and strategy iii) is upper bounded by the discord of formation of the preshared state. What's more, we show that strategy ii) has no advantage over strategy i) in the weak converse regime. As examples, we derive these capacities analytically by the above strategies for some fundamental quantum channels. In some cases, the capacity of strategy iii) is strictly larger than those of strategies i) and ii) whenever entanglement assistance is available. Our results witness the power of random permutation in entanglement-assisted classical communication.

Published in .

Quantification of Unextendible Entanglement and Its Applications in Entanglement Distillation

Sun, 21 Jun 2020 00:00:00 +0000

New Research on the Resource Theory of Quantum Channels

Sun, 12 Apr 2020 00:00:00 +0000

The research achievement has been reported in the official website of .

Recent research by a team at Southern University of Science and Technology (SUSTech) introduced a new resource theory of quantum channels and applied it to study communication over quantum channels.

Shenzhen Institute for Quantum Science and Engineering (SIQSE) Chief Research Scientist and Institute of Electrical and Electronic Engineers (IEEE) Fellow Masahito Hayashi worked with his collaborators to introduce a new resource theory of quantum channels relevant to communication scenarios. The research was published in the high-impact academic journal Physical Review Letters (PRL) under the title, “Application of the Resource Theory of Channels to Communication Scenarios”.

Quantum resource theories offer a highly versatile and powerful framework for studying different phenomena in quantum physics. However, a common criticism is that the framework often ends up with a formalistic level not solving existing problems. In particular, it has been elusive whether the resource theory of quantum channels would be helpful for answering concrete problems at all.

On the other hand, entanglement-assisted information transmission via quantum channel has been a major field of research in quantum information theory at all times. Its central goal is to understand how much of the resources are required to accomplish the desired information transmission by utilizing quantum entanglement.

Quantum entanglement is known as a resource of magical power of quantum system. The aim clarifies how entanglement enhances information transmission, while analyzing this improvement is notoriously difficult due to their complex structures. This motivates the question of whether we can adopt the quantum resource theory framework to investigate the improvement of information transmission by using entanglement, consolidating it as effective tools to solve concrete problems.

Masahito Hayashi and his collaborators took the first step in this direction. They introduced the resource theory of communication, a resource theory of channels relevant to communication via quantum channels. With this formalism, they successfully characterized fundamental properties of a quantum channel as a communication mean: how much information the channel can reliably send (channel capacity) under the efficient use of entanglement and how hard it is to effectively implement the channel (channel simulation cost).

The introduced framework allowed them to employ several novel ideas and techniques that have recently been developed in the study of resource theories to address the “classic” problems in quantum information theory. In particular, they extended the results on the operational characterization of resource theories and obtained an important property known as the strong converse property, which shows the ultimate limitation of the amount of information transmission under the efficient use of entanglement, as well as characterized its channel simulation cost by formulating it as a resource transformation task in the proposed resource theory.

They further showed that their resource theory has an intimate connection to the communication with help of ultimate correlation allowed by causal theories respecting the theory of relativity, suggesting that their framework may serve as an effective theoretical platform to investigate fundamental limitation of communication over quantum channels.

This research shed new perspective to fundamental problems in quantum Shannon theory while lifting the resource theory of channels to effective tools in addressing concrete problems. The technique formalized is extendable to more generic settings thanks to the systematic nature of the resource theory framework.

Ryuji Takagi, a Ph.D. student at Massachusetts Institute of Technology (MIT), was the first author of the paper. Ryuji Takagi, Kun Wang (SIQSE), and Masahito Hayashi were the corresponding authors. SUSTech was the second affiliation.

Paper link:

Entanglement Detection via Direct-Sum Majorization Uncertainty Relations

Thu, 16 Jan 2020 00:00:00 +0000