Entropy

Entangled Qubit States and Linear Entropy in the Probability Representation of Quantum Mechanics

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

Published Apr 9, 2022• 12 citations

Abstract

The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.

DOI: 10.3390/e24040527

Related papers

Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics

Margarita A. Man’ko, Vladimir I. Man’ko

The superposition of pure quantum states explicitly expressed in terms of a nonlinear addition rule of state density operators is reviewed. The probability representation of density matrices of qudit states is used to formulate the interference of the states as a combination of the probability distributions describing pure states. The formalism of quantizer–dequantizer operators is developed. Examples of spin-1/2 states and f-oscillator systems are considered.

Open Systems & Information DynamicsSep 1, 20192 citations

Probability Distributions Describing Qubit-State Superpositions

Margarita A. Man’ko, Vladimir I. Man’ko

We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.

EntropySep 22, 20236 citations

Observables, interference phenomenon and Born’s rule in the probability representation of quantum mechanics

Margarita A. Man’ko, Vladimir I. Man’ko

The description of quantum states by probability distributions of classical-like random variables associated with observables is presented. An invertible map of the wave functions and density matrices onto the probability distributions is constructed. The relation of the probability distributions to quasidistributions like the Wigner function is discussed. The interference phenomenon and superposition principle of pure quantum states are given in the form of nonlinear addition of the probabilities identified with the quantum states. The probability given by Born’s rule is expressed as a function of the probabilities describing the system states. The suggested probability representation of quantum mechanics is presented using examples of harmonic oscillators and qubits.

International Journal of Quantum InformationJan 31, 202011 citations

Superposition rule and entanglement in diagonal and probability representations of density states

Vladimir I. Man’ko, Giuseppe Marmo, E. C. G. Sudarshan

The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the probability representation of quantum mechanics is reviewed. The connection of the diagonal and probability representations is discussed. The superposition rule is considered in terms of the density-operator symbols. The separability and entanglement properties of multipartite quantum systems are formulated as the properties of the density-operator symbols of the system states.

arXiv:0902.4351Physica ScriptaJul 1, 20090 citations

Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

Igor Ya. Doskoch, Margarita A. Man’ko

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

Quantum ReportsSep 26, 201912 citations

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

Matyas I. Mechler, Margarita A. Man’ko, Vladimir I. Man’ko +1 more

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.

EntropyMay 31, 20248 citations