Characterization of Decoherence-Free Subsystems

Daniel A. Lidar, K. Birgitta Whaley

Jonathan L. Ball, Konrad Banaszek

We discuss the structure of decoherence-free subsystems for a bosonic channel affected by collective depolarization. A single use of the channel is defined as a transmission of a pair of bosonic modes. Collective depolarization consists in a random linear U(2) transformation of the respective mode operators, which is assumed to be identical for N consecutive uses of the channel. We derive a recursion formula that characterizes the dimensionality of available decoherence-free subsystems in such a setting.

Naoki Yamamoto

This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrödinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.

Piotr Marecki

H. T. Quan, Zhijun Song, Xiaobao Liu +2 more

S. Siddiqui, Julio R. Gea-Banacloche

We study the performance of the 3-qubit decoherence-free subsystem and the 4-qubit decoherence-free subspace in the presence of partially correlated noise. We characterize their performance in terms of the average and worst-case fidelity, as a function of the ratio of the interqubit distance to the correlation length of the noise, and find that, in general, more symmetric arrangements (triangles or squares) lead to better performance. Overall, we find the 3-qubit code to perform better than the 4-qubit code by about a factor of 2 in the average infidelity. We observe that this is related to the greater robustness of this code against uncorrelated (independent) errors.