Probability representation of quantum observable and quantum states

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.

References in corpus (6)

• Star products, duality and double Lie algebras
• Metric on the space of quantum states from relative entropy. Tomographic reconstruction
• Triangle geometry of the qubit state in the probability representation expressed in terms of the triada of Malevich's Squares
• Generalized tomographic maps
• Does The Uncertainty Relation Determine The Quantum State?
• Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces

Cited by in corpus (11)

• Geometry and Entanglement of Two-Qubit States in the Quantum Probabilistic Representation
• Probability representation of quantum dynamics using pseudostochastic maps
• God plays coins or superposition principle for classical probabilities in quantum suprematism representation of qubit states
• Correlations in a system of classical--like coins simulating spin-1/2 states in the probability representation of quantum mechanics
• Probability representation of quantum states as a renaissance of hidden variables -- God plays coins
• Quantum suprematism picture of Malevich's squares triada for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics
• A New Mechanism of Open System Evolution and Its Entropy Using Unitary Transformations in Noncomposite Qudit Systems
• Qubit representation of qudit states: correlations and state reconstruction
• Dichotomic probability representation of quantum states
• Spin kinetic equations in the probability representation of quantum mechanics
• Probability representation of photon states and tomography