Weak Measurement of Berry's Phase
arXiv:2104.06227 · doi:10.1088/1751-8121/ac20ec
Abstract
Quantum measurements can be generalized to include complex quantities. It is possible to relate the quantum weak values of projection operators to the third order Bargmann invariants. The argument of the weak value becomes, up to a sign, equal to the Berry's phase associated with the three state vectors. In case of symmetric informationally complete, positive operator valued measures (SIC-POVMs), this relation takes a particularly simple form. Alternating strong and weak measurements can be used to determine Berry's phase directly, which demonstrates that not only their real and imaginary parts but also moduli and arguments of weak values have a physical significance. For an arbitrary projection operator, weak value is real when the projector, pre- and post-selected states lie on a so-called null phase curve which includes the geodesic containing the three states as a special case.
arXiv comment8 pages, no figures
References in corpus (13)
- Symmetric Informationally Complete Quantum Measurements
- Quantum-Bayesian Coherence: The No-Nonsense Version
- The significance of the imaginary part of the weak value
- SIC~POVMs and Clifford groups in prime dimensions
- Weak value beyond conditional expectation value of the pointer readings
- Quantum interference experiments, modular variables and weak measurements
- Contextual-value approach to the generalized measurement of observables
- Bargmann Invariants and Geometric Phases - a Generalised Connection
- Geometric phase in weak measurements
- Products of weak values: uncertainty relations, complementarity and incompatibility
- Geometrical aspects of weak measurements and quantum erasers
- Interferences in quantum eraser reveal geometric phases in modular and weak values
- Spikes in quantum trajectories