General QuasiJoint Probabilities on FiniteState Quantum Systems
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Advantages of the Kirkwood–Dirac distribution among general quasiprobabilities for finitestate quantum systems
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2024, 023A02 (2024).
This study investigates the properties of general quasijoint probability distributions in finitestate quantum systems, revealing the KirkwoodDirac distribution as among the most favorable. This highlights the importance of complex distributions in understanding quantum probability.
In quantum mechanics, quantum observables, like position, momentum, energy, and spin, are in general noncommutative, meaning that their measurement order may affect the outcome. As a result, it is generally impossible to measure them simultaneously. Consequently, their joint probability distributions cannot be defined, limiting a complete understanding of quantum systems.
There have been many attempts to address this limitation through their quantum analogues called quasijoint probability distributions, or quasiprobability distributions for short, which extend probability distributions to the negative or the complex domain, where probabilities can take negative or complex values. However, research on quasiprobability distributions of generic quantum systems beyond the positionmomentum pair remains limited.
Addressing this gap, a new study published in Progress of Theoretical and Experimental Physics investigated the properties of all possible quasiprobability distributions in finitestate systems by utilizing the general framework of quasiprobability distributions developed by Lee and Tsutsui. The study especially assessed their properties in two and threestate systems for arbitrary combinations of quantum observables based on two criteria.
The first criterion evaluates the distinguishability of quantum states by quasiprobability distributions using the minimum number of observables. On the other hand, the second criterion assesses their affinity to traditional quantum distributions. This refers to quasiprobability distributions with nonzero values beyond the possible observable values, thus deviating from traditional distributions.
The study found that the KirkwoodDirac distribution is particularly favorable over others. Specifically, it requires only two, instead of three, observables to distinguish all quantum states in twostate systems. Their imaginary nature plays a key role in this regard. Moreover, this distribution is the only one that satisfies the second criterion, facilitating an intuitive explanation of quantum systems.
These results suggest that, contrary to previous belief, complexvalued, instead of real, quasiprobability distributions, can be key to understanding the probabilistic nature of the quantum world.
Advantages of the Kirkwood–Dirac distribution among general quasiprobabilities for finitestate quantum systems
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2024, 023A02 (2024).
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