arXiv:quant-ph/0406070 · Journal of Physics A Mathematical and General

Optimal estimation of one-parameter quantum channels

Mohan Sarovar, Gerard J Milburn

Published Jun 14, 2006• 57 citations

Abstract

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

DOI: 10.1088/0305-4470/39/26/015

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arXiv:quant-ph/0406070 · Journal of Physics A Mathematical and General

Optimal estimation of one-parameter quantum channels

Mohan Sarovar, Gerard J Milburn

Published Jun 14, 2006• 57 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/39/26/015

Related papers

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We study the role of ancillary entanglement in quantum channel parameter estimation and investigate the minimal ancilla dimension required to achieve the maximum Fisher information. We introduce the

k

-ancilla Fisher information, which quantifies the optimal estimation precision achievable with input states of rank at most

k

, and derive a variational characterization in terms of a rank-constrained optimization problem. This formulation leads to a simple characterization of the minimum ancilla dimension

k^*

required for optimal estimation, given by the minimum rank among the maximizers of the associated variational problem. We further identify sufficient conditions under which ancillary entanglement provides no advantage, including channel families admitting a fixed measure-and-prepare representation and channels satisfying a natural horizontality condition. In addition, we derive a bound on the incremental gain in Fisher information obtained by increasing the ancilla dimension under suitable structural assumptions on the optimal input states. The general results are illustrated through explicit examples, including unitary channels, qubit depolarizing and amplitude damping channels. These results provide a systematic framework for understanding and quantifying the entanglement resources required for optimal quantum channel estimation.