Relative states, quantum axes and quantum references

Abstract

We address the problem of measuring the relative angle between two "quantum axes" made out of N1 and N2 spins. Closed forms of our fidelity-like figure of merit are obtained for an arbitrary number of parallel spins. The asymptotic regimes of large N1 and/or N2 are discussed in detail. The extension of the concept "quantum axis" to more general situations is addressed. We give optimal strategies when the first quantum axis is made out of parallel spins whereas the second is a general state made out of two spins.

6 pages, no figures

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• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Relativistic quantum information theory and quantum reference frames
• Testing identity of collections of quantum states: sample complexity analysis