Optimal phase estimation in quantum networks

Abstract

We address the problem of estimating the phase phi given N copies of the phase rotation u(phi) within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimise the POVM for a given input state and fixed arrangement. Then we also optimise the input state for some specific cost functions. In all cases, the optimal POVM is equivalent to a quantum Fourier transform in an appropriate basis. Examples and applications are given.

9 pages, 2 figures; this is an extended version of arXiv:quant-ph/0609160. v2: minor corrections in references

References in corpus (6)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum metrology
• Quantum Algorithms Revisited
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Optimal quantum circuits for general phase estimation
• A Lower Bound for Quantum Phase Estimation

Cited by in corpus (8)

• Elucidating Reaction Mechanisms on Quantum Computers
• On the relationship between continuous- and discrete-time quantum walk
• Quantum algorithms for algebraic problems
• Public-key cryptography based on bounded quantum reference frames
• Coherence as a resource for phase estimation
• Optimal quantum metrology under energy constraints
• Unconditionally-secure and reusable public-key authentication
• Quantum Signal Processing and Quantum Singular Value Transformation on $U(N)$