Von Neumann entropy is a measure of the quantum mechanical uncertainty or mixedness of a quantum state, analogous to the classical Shannon entropy for probability distributions. It is defined as the trace of the product of the density matrix and the logarithm of the density matrix, providing insights into quantum information and entanglement properties of the system.

Von Neumann Entropy

Von Neumann entropy

quantum mechanical uncertainty

mixedness of a quantum state

classical Shannon entropy

Probability distributions describe how the values of a random variable are distributed, providing a mathematical function that assigns probabilities to each possible outcome. They are essential in statistics and data analysis for modeling uncertainty and making predictions about future events or data patterns.

probability distributions

trace of the product

A density matrix is a mathematical representation used in quantum mechanics to describe the statistical state of a quantum system, encompassing both pure states and mixed states. It provides a complete description of the system's statistical properties, allowing for the calculation of expectation values and probabilities for various measurements.

density matrix

logarithm of the density matrix

Quantum information explores the encoding, processing, and transmission of information using the principles of quantum mechanics, offering revolutionary approaches to computation and communication. It leverages phenomena like superposition and entanglement to perform operations beyond the capabilities of classical systems.

quantum information

entanglement properties

A quantum state is a mathematical object that fully describes a quantum system, encapsulating all its possible information, such as position, momentum, and spin. It is typically represented by a wave function or a state vector in a complex Hilbert space, and its evolution is governed by the Schrödinger equation.

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