Quantifying total correlations in quantum systems through the Pearson correlation coefficient

• URL: http://arxiv.org/abs/2306.14458v3
• Date: Tue, 2 Jul 2024 05:33:22 GMT
• Title: Quantifying total correlations in quantum systems through the Pearson correlation coefficient
• Authors: Spyros Tserkis, Syed M. Assad, Ping Koy Lam, Prineha Narang,
• Abstract summary: We show 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.
• Score: 0.23999111269325263
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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