Measuring the projective-unitary invariant properties of a set of states, and applications

Abstract:

The geometrical arrangement of a set of quantum states in projective Hilbert space can be found using relational information only. This information is encoded in the overlaps between pairs of states, as well as in higher-order Bargmann invariants encoding the relative orientation of n>2 states. We describe how to measure these invariants with a generalization of the SWAP test, and how to pool the information to obtain a complete characterization of their projective-unitary invariant properties. As applications, we describe basis-independent tests for linear independence, coherence, and for the presence of complex-valued amplitudes (“imaginarity”). We also describe how higher-order invariants can be used to certify multi-system indistinguishability. This is joint work with Michal Oszmaniec and Daniel Brod.

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Zoom meeting details 

Topic: Quantum Information and Quantum Computing Working Group
Time: May 06, 2021, 3:15 PM Warsaw
 
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https://tinyurl.com/ctp-quantum

Meeting ID: 96294497969
Passcode: 729533

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