skip to main content

Title: Process tomography for unitary quantum channels

We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary channel acting on a d-level quantum system can be uniquely identified among all other channels (unitary or otherwise) with only O(d{sup 2}) interactive observables, as opposed to the O(d{sup 4}) required for tomography of arbitrary channels. This result generalizes to the problem of identifying channels with at most q Kraus operators, and slight improvements can be obtained if we wish to identify such a channel only among unital channels or among other channels with q Kraus operators. These results are proven via explicit construction of large subspaces of Hermitian matrices with various conditions on rank, eigenvalues, and partial trace. Our constructions are built upon various forms of totally nonsingular matrices.
Authors:
 [1] ;  [2]
  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada)
  2. Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
Publication Date:
OSTI Identifier:
22250882
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; HERMITIAN MATRIX; TOMOGRAPHY