Finding the trade-off relationships between key parameters of quantum communication systems. In particular, my recent interests are focusing on error exponent analysis of quantum source and channel coding.  

Refs:

1. Cheng, Hanson, Datta, Hsieh. Duality between source coding with quantum side information and c-q channel coding. arXiv:1809.11143 (2018). 

2. Cheng & Hsieh. On the Concavity of Auxiliary Function in Classical-Quantum Channels. IEEE Trans. Inf. Theory, 62(10), 5960 - 5965, 2016.

3. Cheng & Hsieh. Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing. IEEE Transactions on Information Theory, vol. 64, no. 2, pp. 1385-1403 (2018).  

I am generally interested in classical/quantum statistical learning models; namely, to understand the generalization errors of different learning settings. I also have interest in understanding how quantum computation (and quantum entanglement) can speed up the machine learning tasks. 

Refs: 

1. Du, Hsieh, Liu, Tao. Implementable Quantum Classifier for Nonlinear Data. arXiv:1809.06056 (2018).

2. Cheng, Hsieh and Yeh. The Learnability of Unknown Quantum Measurements. QIC, Vol. 16, No. 7-8, 0615-0656, 2016.

I am interested in studying physics foundations in views of resource theory, or problems where I can apply quantum information techniques. 

Refs: 

1. Vijayan, Chitambar, Hsieh. One-shot assisted concentration of coherence. Journal of Physics A: Mathematical and Theoretical, Vol. 51, No. 41, p. 414001 (2018). [arXiv:1804.06554]

2. ​Anshu, Hsieh, Jain. Quantifying resource in catalytic resource theory. Physical Review Letters, Accepted on 17-July-2018.  arXiv:1708.00381 (2017). 

3. Chitambar & Hsieh. Relating the Resource Theories of Entanglement and Quantum Coherence. Phys. Rev. Lett. 117, 020402 (2016).

4. Lee, Hsieh, Flammia and Lee. Local PT symmetry violates the no-signaling principle. Phys. Rev. Lett. 112, 130404 (2014).

Finding the secrecy structure in a classical probability distribution/bipartite quantum state, and its relationship to quantum entanglement: 

Refs:

1. Chitambar, Fortescue & Hsieh. Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information. Advances in Cryptology -- CRYPTO 2015, Volume 9216 of the series Lecture Notes in Computer Science pp. 443-462, 2015.

2. Chitambar, Fortescue & Hsieh. A Classical Analog to Entanglement Reversibility. Phys. Rev. Lett. 115, 090501, 2015.

3. Chitambar, Fortescue & Hsieh. Quantum Versus Classical Advantages in Secret Key Distillation. ArcticCrypto 2016.

These mathematical components commonly appear in my  outcomes, and development of deeper knowledge in these areas allows me to carry out these proposed new directions.  

Refs:

1. Zhang, Gao, Hsieh, Hang, Tao. Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization. arXiv:1809.00781 (2018).

2. Cheng & Hsieh. Characterizations of matrix and operator-valued Φ-entropies, and operator Efron–Stein inequalities. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 472, no. 2187, p. 20150563 (2016).