Quantum Mutual Information

In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state.

Version

v1 · 2026-09-28 · History

Domain-specific #

11611

Domain group

Formal Sciences

Origin domain

Information Theory

Subdomain

Quantum Information Theory → Information Theory

Core Idea

Quantum Mutual Information is treated here as the recurring computer science and information systems identity summarized by this source-grounded definition: In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual information.

Scope of Application

• Motivation. For simplicity, it will be assumed that all objects in the article are finite-dimensional.

• Motivation. The definition of quantum mutual entropy is motivated by the classical case.

• Motivation. For a probability distribution of two variables p(x, y), the two marginal distributions are.

• Motivation. p(x) = \sum{y} p(x,y), \qquad p(y) = \sum{x} p(x,y).

• Motivation. I(X:Y) = S(p(x)) + S(p(y)) - S(p(x,y)).

Clarity

A clear use of Quantum Mutual Information names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state.

Manages Complexity

Quantum Mutual Information compresses multiple computer science and information systems details into a stable diagnostic relation. The source shows both the central mechanism—for a probability distribution p(x,y), the marginal distributions are obtained by integrating away the variables x or y.—and the practical consequence—i(X:Y) = S(p(x)) + S(p(y)) - S(p(x,y)).

Abstract Reasoning

1. Type the carrier. Identify the computer science and information systems entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state.
3. Check operation and conditions. For simplicity, it will be assumed that all objects in the article are finite-dimensional.
4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Quantum Mutual Information transfers literally when a new case preserves the same carrier type, relation, and recognition test. For simplicity, it will be assumed that all objects in the article are finite-dimensional. The definition of quantum mutual entropy is motivated by the classical case. Beyond the home domain. No canonical parent is asserted for Quantum Mutual Information. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Neighborhood in Abstraction Space

Quantum Mutual Information sits in a moderately populated region (57^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Quantum States & Information Measures (25 abstractions)

Nearest neighbors

• Observable — 0.86
• Mean-field theory — 0.86
• Characteristic state function — 0.86
• Quantum Fisher information — 0.85
• Big O in probability notation — 0.84

Computed from structural-signature embeddings · 2026-10-08