Quantum state-space is characterized by fixed 2-norm and 3-norm constraints for pure states and a variance lower bound for all states, using only probabilities from a single complex-projective 3-design reference measurement.
Measuring relational information between quantum states, and applications
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abstract
The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable generalizations of the SWAP test. This allows for a complete and robust characterization of the projective-unitary invariant properties of any set of pure or mixed states. As applications, we describe basis-independent tests for linear independence, coherence, and imaginarity. We also show that Bargmann invariants can be used to characterize multi-photon indistinguishability.
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Characterizing quantum state-space with a single quantum measurement
Quantum state-space is characterized by fixed 2-norm and 3-norm constraints for pure states and a variance lower bound for all states, using only probabilities from a single complex-projective 3-design reference measurement.