Standard symmetrized variance with applications to coherence,
uncertainty and entanglement
- URL: http://arxiv.org/abs/2207.06048v1
- Date: Wed, 13 Jul 2022 08:43:59 GMT
- Title: Standard symmetrized variance with applications to coherence,
uncertainty and entanglement
- Authors: Ming-Jing Zhao, Lin Zhang, and Shao-Ming Fei
- Abstract summary: We consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state.
We show that the standard symmetrized variance is also an entanglement measure for bipartite systems.
- Score: 3.7298088649201353
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Variance is a ubiquitous quantity in quantum information theory. Given a
basis, we consider the averaged variances of a fixed diagonal observable in a
pure state under all possible permutations on the components of the pure state
and call it the symmetrized variance. Moreover we work out the analytical
expression of the symmetrized variance and find that such expression is in the
factorized form where two factors separately depends on the diagonal observable
and quantum state. By shifting the factor corresponding to the diagonal
observable, we introduce the notion named the standard symmetrized variance for
the pure state which is independent of the diagonal observable. We then extend
the standard symmetrized variance to mixed states in three different ways,
which characterize the uncertainty, the coherence and the coherence of
assistance, respectively. These quantities are evaluated analytically and the
relations among them are established. In addition, we show that the standard
symmetrized variance is also an entanglement measure for bipartite systems. In
this way, these different quantumness of quantum states are unified by the
variance.
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