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  • Writer's pictureMin-Hsiu Hsieh

Quantum Cryptography

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.

Selected Contributions:
  • 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.

  • 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.

  1. ​Eric Chitambar and Min-Hsiu Hsieh. Round Complexity in the Local Transformations of Quantum and Classical States. Nature Communications (accepted on 9 August 2017). [arXiv:1610.01998]

  2. Eric Chitambar, Min-Hsiu Hsieh, Andreas Winter. The Private and Public Correlation Cost of Three Random Variables With Collaboration. IEEE Transactions on Information Theory, vol. 62, no. 4, pp. 2034–2043 (2016). [arXiv:1411.0729]

  3. Eric Chitambar, Ben Fortescue, and Min-Hsiu Hsieh. A classical analog to entanglement reversibility. Physical Review Letters, vol. 115, p. 090501 (2015). [arXiv:1502.04433]

  4. Mark Wilde and Min-Hsiu Hsieh. Public and private resource trade-offs for a quantum channel. Quantum Informa- tion Processing, vol. 11, pp. 1465–1501 (2012). [arXiv:1005.3818]

  5. Min-Hsiu Hsieh and Mark Wilde. Public and private communication with a quantum channel and a secret key. Physical Review A, vol. 80, no. 2, p. 022306 (2009). [arXiv:0903.3920]

  6. Min-Hsiu Hsieh, Zhicheng Luo, and Todd Brun. Secret-key-assisted private classical communication capacity over quantum channels. Physical Review A, vol. 78, no. 4, p. 042306 (2008). [arXiv:0806.3525]

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