Fast rate estimation of an unitary operation in SU(d)

Abstract

We give an explicit procedure based on entangled input states for estimating a $SU(d)$ operation $U$ with rate of convergence $1/N^2$ when sending $N$ particles through the device. We prove that this rate is optimal. We also evaluate the constant $C$ such that the asymptotic risk is $C/N^2$. However other strategies might yield a better const ant $C$.

8 pages, 1 figure Rewritten version, accepted for publication in Phys. Rev. A. The introduction is richer, the "tool section" on group representations has been suppressed, and a section proving that the 1/N^2 rate is optimum has been added

References in corpus (2)

• Multiphoton path entanglement by non-local bunching
• Quantum metrology at the Heisenberg limit with ion traps

Cited by in corpus (2)

• Parameter Estimation with Mixed-State Quantum Computation
• Channel Estimation Theory of Low-Noise Multiple Parameters:Attainablity Problem of the Cram{é}r-Rao Bounds