Contributions to the Field

 
Quantum
Error
Correction
One of the most important discoveries in quantum information science was the existence of QECCs in 1995. Up to that point, there was a widespread belief that environmental noise would doom any chance of building large scale quantum computers or quantum communication protocols. The discovery of the first QECC defied these expectations, and was quickly followed by the development of the theory of stabiliser codes, thereby drawing on the well-studied theory of classical error correction. However, the connection between classical codes and quantum codes was not universal. Rather, only a subset of classical codes that satisfied a certain constraint could be used to construct quantum codes.
Full Publications in This Area. 
Selected Contributions:
  1. In [Science 314:436-439 (2006)] my collaborators and I developed a methodology that generalises the stabilizer codes. Our result showed that, with the assistance of prior shared entanglement, every classical linear code can be used to construct a corresponding quantum code (the entanglement-assisted quantum error correcting code, EAQECC). This research confirms, for the first time, that QECCs are more general and include classical error-correcting codes as a special case, and significantly advances the theory of QECCs. 

    • This result has become a book chapter in the textbook “Quantum Error Correction”, Cambridge University Press, August 2013.

  2. In [IEEE TIT 57:1761–1769 (2011)] I, together with Yen and Hsu, constructed families of high performance EAQECCs with very little pre-shared entanglement. This result disproved the conjectured weakness of EAQECCs—that the high performance requires massive consumption of maximally entangled states.-

    • Our construction made use of combinatorial design theory, and triggered a significant amount of follow-up research in that area.

Quantum
Shannon
Theory
Quantum Shannon theory has emerged in recent years as the quantum generalisation of Shannon’s information theory. Although the study of quantum Shannon theory is heavily motivated by similar ideas in classical Shannon theory, almost none of the major results were obtained by trivial generalisation of the corresponding ones in the classical setting. The non-commutative nature of quantum channels and states causes many seemingly trivial problems in classical information theory to become highly formidable. To make progress, many basic tools in the classical setting have been revised into the corresponding non-commutative form of suitable operator structures. Moreover, the theory of quantum channels is richer, and includes several distinct capacities that depend on the type of information being sent and the additional resources being used. 
Full Publications in This Area. 
Selected Contributions:
  1. In [IEEE TIT 59:615–630 (2013)] I established a quantum rate distortion theory with Datta and Wilde that governs the optimal trade-offs between the compression rate of a quantum source and the given distortion. This result resolved one of the most important capacity theorems remaining in quantum information theory.

  2. In [IEEE TIT 56:4682-4704 (2010)] and [IEEE TIT 56:4705-4730 (2010)], Wilde and I proved one of the most general capacity theorems of a quantum channel which involves the generation of and/or assistance from three most commonly used resources in the theory of quantum information, namely, classical communication, quantum communication, and entanglement. Wilde and I developed a protocol that allowed us to simultaneously transmit both classical and quantum information over a quantum channel with entanglement assistance.

    • Our research became the content of several sections in the textbook "Quantum Information Theory," Cambridge University Press (ISBN: 9781107034259), May 2013. 

Quantum
 & Classical keys
One of the earliest breakthroughs in quantum cryptography was the discovery of a protocol by Bennett and Brassard in 1984 for establishing secret keys through a quantum channel. This is now well known as quantum key distribution (QKD). This thriving area of research has resulted in currently available quantum technology, and efforts are now under way to construct space-to-ground quantum communication devices. These initial results on QKD have also inspired the information-theoretic study of secret communication over quantum channels; that is, to determine the fundamental limit of private communication through a quantum channel. Devetak was the first to establish the private capacity of a quantum channel as one of its fundamental capacities.
​Full Publications in This Area.
Selected Contributions:
  1. In [CRYPTO 2015-pp. 443-462], we considered the problem of extracting secret keys from an eavesdropped source at a rate given by the conditional mutual information, and gave results under different scenarios.The two referees from CRYPTO 2015 commented in their reports: 

    • #1: This paper addresses a classical (old) problem in information-theoretic cryptography in a nice way and manages to give new insights (at least for specific distributions) into the task of optimal secret key agreement. 

    • #2: The paper investigates an important task in information theoretic cryptography and manages to shed new light on certain aspects. To be more precise, the authors succeed in showing conditions on a tripartite distribution p_XYZ under which the conditional mutual information coincides with the secret key rate — under several different extra assumptions.

  2. In [Phys. Rev. Lett. 115: 090501 (2015)], Chitambar, Fortescue and I studied the problem of secrecy reversibility. This asks when two honest parties can distil secret bits from some tripartite distribution p_XYZ and transform secret bits back into p_XYZ at equal rates using local operation and public communication. We identified the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution.

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​University of Technology Sydney

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min-hsiu.hsieh (at) uts.edu.au

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