Current students

Sample-optimal tomography of quantum states

Nengkun Yu, IQC

It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error ϵ in trace distance required O(dr2/ϵ2) copies for a d-dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O((dr/δ)ln(d/δ)) copies of ρ to error δ in infidelity, and a matching lower bound up to logarithmic factors.

Towards demonstration of Majorana-based topological qubits

Karsten Flensberg, Niels Bohr Institute

The first part of the talk presents recent progress in the search for condensed matter systems hosting Majorana bound state in semiconductor-superconductor nanowire-based heterostructures. In the second part a proposal for the next steps towards manipulation of quantum information stored in topological qubits is presented.

Join us at the Institute for Quantum Computing for a two-week introduction to the theoretical and experimental study of quantum information processing.

Applications of order isomorphisms of C*-algebras

Fred Shultz, Wellesley College

We will review known results about order isomorphisms of C*-algebras,
and will describe some applications to complete positivity of maps and
a generalization of the Choi matrix. (This is joint work with Vern Paulsen.)
Then we will describe some applications to quantum information theory.

How hard is deciding trivial versus non-trivial in the dihedral coset problem

Nai-Hui Chia, Pennsylvania State University

The dihedral coset problem (DCP) is an important open problem in quantum algorithms and has been studied since the early days of quantum computing. This problem attracts attention even from experts in cryptography due to its application to the lattice-based cryptosystems. It has been shown by Oded Regev in 2005 that the DCP has deep connections to the unique shortest vector problem and the random subset sum problem.

A deterministic polynomial time algorithm for word problem for the free skew field

Ankit Garg, Princeton University

We study the word problem for the free skew field of non-commutative rational functions. We prove that an existing algorithm due to Gurvits is actually a deterministic polynomial time algorithm for this problem (over the rationals). Our analysis is simple, providing explicit bounds on the "capacity'' measure of totally positive operators introduced by Gurvits.

Measurement-induced localization of an ultracold lattice gas

Mukund Vengalattore, Cornell University

The act of observation has profound consequences on a quantum system. I will describe our experimental demonstration of a Heisenberg microscope based on nondestructive imaging of a lattice gas. We show that the act of imaging these atoms induces their localization - a manifestation of the quantum Zeno effect.