Quantifying total correlations in quantum systems through the Pearson correlation coefficient
arXiv (Cornell University)(2023)
摘要
Conventionally, the total correlations within a quantum system are quantified
through distance-based expressions such as the relative entropy or the
square-norm. Those expressions imply that a quantum state can contain both
classical and quantum correlations. In this work, we provide an alternative
method to quantify the total correlations through the Pearson correlation
coefficient. Using this method, we argue that a quantum state can be correlated
in either a classical or a quantum way, i.e., the two cases are mutually
exclusive. We also illustrate that, at least for the case of two-qubit systems,
the distribution of the correlations among certain locally incompatible pairs
of observables provides insight in regards to whether a system contains
classical or quantum correlations. Finally, we show how correlations in quantum
systems are connected to the general entropic uncertainty principle.
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关键词
total correlations,quantum systems
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