Covariant quantum measurements may not be optimal

Abstract

Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not be a covariant measurement (contrary to widespread belief). It may be advantageous for the receiver to use a different group and an indirect estimation method: first, an ordinary measurement supplies redundant numerical parameters; the latter are then used for a nonlinear optimal identification of the signal.

minor corrections, to appear in J. Mod. Opt. (proc. of Gdansk conf.)

References in corpus (2)

• Transmission of a Cartesian Frame by a Quantum System
• Aligning Reference Frames Using Quantum States

Cited by in corpus (13)

• Reference frames, superselection rules, and quantum information
• Efficient use of quantum resources for the transmission of a reference frame
• Optimal estimation of group transformations using entanglement
• Quantum reverse-engineering and reference frame alignment without non-local correlations
• Estimation of pure qubit states with collective and individual measurements
• Entanglement assisted alignment of reference frames using a dense covariant coding
• Query-optimal estimation of unitary channels in diamond distance
• Maximum likelihood estimation for a group of physical transformations
• Elliptic Rydberg states as direction indicators
• Unitary-process discrimination with error margin
• Relative states, quantum axes and quantum references
• Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics
• Agnostic Process Tomography