Optimal phase estimation in quantum networks
ArXiv 0706.4412 (2007)
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.Unifying classical and quantum key distillation.
4th Theory of Cryptography Conference, TCC 2007, Amsterdam, The Netherlands, February 21-24, 2007. Proceedings (Lecture Notes in Computer Science 4392/2007) (2007) 456-478
Optimal quantum circuits for general phase estimation.
Phys Rev Lett 98:9 (2007) 090501
Abstract:
We address the problem of estimating the phase phi given N copies of the phase-rotation gate uphi. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi for phi depends only on the difference phi-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.Optimal quantum circuits for general phase estimation
Physical Review Letters 9 (2007) 0609160
Robust state transfer and rotation through a spin chain via dark passage
ArXiv quant-ph/0702019 (2007)