Geometry and Entanglement of Two-Qubit States in the Quantum Probabilistic Representation

Abstract

A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose (ppt)-criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevich's squares for entangled states of two qubits are defined through the qutrit state, and the critical values of the sum of their areas are calculated. We always find an interval for the sum of the square areas, which provides the possibility for an experimental checkup of the entanglement of the system in terms of the probabilities.

References in corpus (17)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement of a Pair of Quantum Bits
• On the volume of the set of mixed entangled states
• Symplectic tomography as classical approach to quantum systems
• Cloud Quantum Computing of an Atomic Nucleus
• Geometry of quantum systems: density states and entanglement
• Metric on the space of quantum states from relative entropy. Tomographic reconstruction
• Quantum Tomography twenty years later
• Triangle geometry of the qubit state in the probability representation expressed in terms of the triada of Malevich's Squares
• Probability representation of quantum observable and quantum states
• Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
• God plays coins or superposition principle for classical probabilities in quantum suprematism representation of qubit states
• Quantum suprematism picture of Malevich's squares triada for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics
• New entropic inequalities for qubit and unimodal Gaussian states
• The Volume of Two-Qubit States by Information Geometry

Cited by in corpus (6)

• 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
• Majorana representation of adiabatic and superadiabatic processes in three-level systems
• 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
• Coherent states of parametric oscillators in the probability representation of quantum mechanics