Quantum Mechanics in Terms of Symmetric Measurements

Bartel Leenert van der Waerden

Yajing FAN, Xueying Sha

Abstract Quantum coherence is one of the characteristic features of quantum mechanics and underpins many quantum mysteries. In this work, we investigate the average coherence of a quantum state with respect to symmetric positive operator-valued measures using metric-adjusted skew information. Specifically, we derive explicit expressions for the average coherence relative to mutually unbiased measurements and to general symmetric informationally complete measurements, and establish a complementary relation between average coherence and maximal coherence. Furthermore, we introduce a measure of average coherence based on metric-adjusted skew information for states with respect to a generalized symmetric measurements (GSMs). When these GSMs are required to be equinumerous, the corresponding average coherence reduces to that for symmetric measurements. Finally, we evaluate and compare various average coherence measures with different operator monotone functions for qubit states, Werner states, and isotropic states.

K. B. Wharton

We introduce an intuitive particle-based model of time-symmetric quantum physics that gives a concrete description of what goes on in the time between projective measurements of a quantum system. The time-symmetry in this model means that we ...Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to ...

J.P. Elliott, P. G. Dawber

Julian Schwinger

We introduce an intuitive particle-based model of time-symmetric quantum physics that gives a concrete description of what goes on in the time between projective measurements of a quantum system. The time-symmetry in this model means that we ...Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to ...