News & Events

Satish Pandey

Date/Time: 
Thursday, February 25, 2021 - 11:00 to 12:00
Venue: 
SMS Conference Room (via GoogleMeet)
Speaker: 
Satish Pandey
Affiliation: 
Technion - Israel Institute of Technology
Title: 
Entanglement breaking rank and quantum majorization

 In Quantum Information Theory, quantum states and quantum channels are central objects of study. Mathematically, a quantum state is a positive semidefinite matrix of unit trace, and a quantum channel is formalized by a linear map which is completely positive and trace preserving (CPTP).  

In the first part of this talk, we describe a rank function, that we call the ``entanglement breaking rank", of a special class of quantum channels called ``entanglement breaking channels". We show how this rank parameter for a particular channel links to one of the most celebrated problems in frame theory, commonly referred to as Zauner's conjecture. This helps us present an analytic, perturbative approach to the conjecture rather than algebraic. This part of the talk is based on a joint work with Vern Paulsen, Jitendra Prakash (NISER alumnus), and Mizanur Rahaman.

In the second part of this talk, we discuss an ordering of quantum states referred to as ``quantum majorization'', which is a natural generalization of the concept of matrix majorization in the quantum mechanical setting. We shall briefly revisit the work by Gour et al. (Nature Communications, 2018); they established a characterization for majorization of quantum states in the finite-dimensional setting via the notion of conditional min-entropy. We then outline our work where we extend the characterization by Gour et al. to the context of semifinite von Neumann algebras. Our method relies on a connection between the conditional min-entropy and the operator space projective tensor norm for injective von Neumann algebras. This part of the talk is based on a joint work with Priyanga Ganesan (NISER alumnus), Li Gao, and Sarah Plosker.

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