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Quantum expectation value

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Summary

For a state $\rho$ and observable $A$ , the expectation value is $\langle A\rangle_\rho=\operatorname{Tr}(\rho A)$ when defined; for a pure vector state it reduces to $\langle\psi|A|\psi\rangle$ .

Record metadata

Canonical name: Quantum expectation value
Concept ID: quantum_expectation_value
Content version: 2.3.0
Primary field: Physics
Fields: Physics
Primary domain: Quantum mechanics
Domains: Quantum mechanics
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: State-dependent statistical quantity

Concept sources

Wikipedia — Expectation value in quantum mechanics — Expectation value in quantum mechanics · encyclopedic reference · source ID wp-physics-expectation-value
nLab — expectation value — expectation value · mathematical reference · source ID nlab-physics-expectation-value
Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum
NIST — Quantum Physics Theory — Quantum Physics Theory · NIST research reference · source ID nist-quantum-theory

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Density operator Quantum expectation value

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This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: density_to_expectation
Relation type: State / property description state-description
Direction: source → target
Endpoint roles: source: Has state / property description; target: State / property description of
Authored annotation: gives expectation values

Authored explanation

For a density operator $\rho$ , the expectation of an observable $A$ is $\operatorname{Tr}(\rho A)$ whenever the product and trace are defined.

How to interpret this relation type

The target represents a state, property, observable, or state-dependent description associated with the source system or theory.

Relation sources

Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum
Wikipedia — Expectation value in quantum mechanics — Expectation value in quantum mechanics · encyclopedic reference · source ID wp-physics-expectation-value
nLab — expectation value — expectation value · mathematical reference · source ID nlab-physics-expectation-value

Inner-product space Quantum expectation value

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This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: innerproduct_to_expectation
Relation type: Mathematical formulation mathematical-formulation
Direction: source → target
Endpoint roles: source: Mathematically formulates; target: Mathematically formulated using
Authored annotation: pure-state quadratic form

Authored explanation

For a normalized state vector $\psi$ in the domain of $A$ , the pure-state expectation is $\langle\psi,A\psi\rangle$ ; for an unnormalized nonzero vector, divide by $\langle\psi,\psi\rangle$ .

How to interpret this relation type

A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.

Relation sources

Wikipedia — Inner product space — Inner product space · expository · source ID wp-inner-product
nLab — Inner product space — Inner product space · reference · source ID nlab-inner-product-space
Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum

Quantum observable Quantum expectation value

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This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: observable_to_expectation
Relation type: Theory component theory-component
Direction: source → target
Endpoint roles: source: Contributes to; target: Contains theory component
Authored annotation: observable argument

Authored explanation

An expectation value is evaluated for a specified observable in a specified state.

How to interpret this relation type

The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.

Relation sources

Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum
NIST — Quantum Physics Theory — Quantum Physics Theory · NIST research reference · source ID nist-quantum-theory
Wikipedia — Expectation value in quantum mechanics — Expectation value in quantum mechanics · encyclopedic reference · source ID wp-physics-expectation-value

Quantum state Quantum expectation value

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: state_to_expectation
Relation type: Theory component theory-component
Direction: source → target
Endpoint roles: source: Contributes to; target: Contains theory component
Authored annotation: state functional

Authored explanation

A quantum state assigns expectation values to observables; in operator formulations this assignment is a positive normalized functional.

How to interpret this relation type

The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.

Relation sources

Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum
NIST — Quantum Physics Theory — Quantum Physics Theory · NIST research reference · source ID nist-quantum-theory
Wikipedia — Expectation value in quantum mechanics — Expectation value in quantum mechanics · encyclopedic reference · source ID wp-physics-expectation-value

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No direct relations are authored in this direction.

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Quantum expectation value

Summary

Record metadata

Concept sources

Incoming relations (arrows to this concept)

Density operator Quantum expectation value

Authored explanation

How to interpret this relation type

Relation sources

Inner-product space Quantum expectation value

Authored explanation

How to interpret this relation type

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Quantum observable Quantum expectation value

Authored explanation

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Quantum state Quantum expectation value

Authored explanation

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Outgoing relations (arrows from this concept)