Control limit on quantum state preparation under decoherence

Abstract

Quantum information technologies require careful control for generating and preserving a desired target quantum state. The biggest practical obstacle is, of course, decoherence. Therefore, the reachability analysis, which in our scenario aims to estimate the distance between the controlled state under decoherence and the target state, is of great importance to evaluate the realistic performance of those technologies. This paper presents a lower bound of the fidelity-based distance for a general open Markovian quantum system driven by the decoherence process and several types of control including feedback. The lower bound is straightforward to calculate and can be used as a guide for choosing the target state, as demonstrated in some examples. Moreover, the lower bound is applied to derive a theoretical limit in some quantum metrology problems based on a large-size atomic ensemble under control and decoherence.

Bound on the distance between controlled quantum state and target state under decoherence

“…which takes the transition time T = π/(2Ω). Furthermore, we here consider the two types of decoherences; amplitude damping M AD ˆand phase damping M PD ˆ [20]:…”

“…For closed quantum systems, detailed analysis of control limit in various cases have already been investigated [9][10][11][12][13]. Extending these, many studies have been extensively conducted to clarify the limit of control for open quantum systems in recent years [14][15][16][17][18][19][20][21]. However, these results are limited to specific situations and require integration and eigenvalue calculations, which poses the problem of computational difficulties.…”