Probability representation of quantum observable and quantum states
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
TL;DR
This paper develops a probability-based framework for representing quantum observables and states, connecting traditional quantum mechanics with tomographic probability distributions, and explores their dynamics and channels.
Contribution
It introduces a probability representation for quantum observables and states, deriving their evolution equations and quantum channels, providing a new perspective in quantum mechanics.
Findings
Derived the Heisenberg evolution equation in probability representation
Connected quantum states and observables through probability distributions
Presented quantum channels for qubits in the probability framework
Abstract
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation for quantum observables (Heisenberg equation) in the probability representation and give examples of the spin-1/2 (qubit) states and the spin observables. We present quantum channels for qubits in the probability representation.
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