Research

I spent five years as a visiting assistant professor at Bucknell University. I previously held a postdoctoral position at Louisiana State University where I studied the mathematics of quantum information theory with Mark Wilde and the rest of the Quantum Science and Technology Group. I am interested in how ideas from functional analysis can be applied to problems in quantum information. I am also interested in operator algebras and how ideas from harmonic analysis on groups can be extended to locally compact quantum groups.

Before coming to Baton Rouge, I was a postdoc in the Mathematics Department of Universidad Complutense de Madrid, working with the Mathematics and Quantum Information research group lead by David Perez Garcia.

I received my Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign. My thesis advisor was Professor Zhong-Jin Ruan and my thesis title was "Noncommutative L_p-spaces Associated with Locally Compact Quantum Groups". This involved studying the interaction between the quantum group and the structure of the noncommutative L_p-space constructed using the Haar weight.

You can see my Google Scholar profile at this link.

Research Interests:

• • Functional analysis,

  • Operator algebras,

  • Operator spaces,

  • Locally compact quantum groups,

  • Noncommutative Lp spaces,

  • Quantum information theory,

  • Quantum game theory,

  • Quantum many-body systems.

Publications

• Operational Meaning of Quantum Measures of Recovery (with Christoph Hirche, Ciara Morgan, Jonathan P. Olson, Kaushik P. Seshadreesan, Jon Watrous, and Mark M. Wilde, Physical Review A 94 (2), 022310)

• Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication (with Milán Mosonyi, and Mark M. Wilde, Communications in Mathematical Physics 344 (3), 797-829)

• Rank-One Quantum Games (with Marius Junge, Carlos Palazuelos Cabezon, and David Perez Garcia) (computational complexity, 24 (1), 133-196)

• Joint system quantum descriptions arising from local quantumness (with Marius Junge, Miguel Navascues, David Perez Garcia, and Ignacio Villanueva) (Communications in Mathematical Physics 322 (2), 501-513)

• A physical approach to Tsirelson's problem (with Miguel Navascues, David Perez-Garcia, and Ignacio Villanueva) (Foundations of Physics 42 (8), 985-995)

• A Hausdorff-Young inequality for locally compact quantum groups, Internat. J. Math., 21 (2010), no. 12, 1619–1632.

• Noncommutative L_p spaces associated with locally compact quantum groups (Ph.D. thesis)

Available at: http://www.ideals.illinois.edu/handle/2142/16895