Density matrix

A positive semidefinite operator of unit trace that represents a quantum state, including pure states and statistical mixtures. It determines expectation values for all measurements on the system.

Pure state: A quantum state described by a single state vector, with no statistical uncertainty about which state was prepared. A rank-one density matrix represents a pure state.
Hilbert space: A complete inner-product vector space used to represent quantum states and observables. Density operators act on the Hilbert space of the system.
Quantum tomography: Methods for reconstructing an unknown quantum state from measurement data. Tomography estimates the density matrix from outcomes across suitable measurements.
Wavefunction: A complex-valued function encoding a quantum system's pure-state amplitudes in a chosen representation. A wavefunction specifies a pure state, whereas density matrices also accommodate mixtures.
Mixed state: A quantum state that is a statistical mixture of distinguishable pure-state preparations. A density matrix represents mixtures without choosing one constituent state as the actual state.
Trace: The sum of an operator's diagonal elements in an orthonormal basis, invariant under basis changes. Unit trace normalizes a density matrix and its measurement probabilities.
Quantum decoherence: The loss of observable quantum interference through a system's interaction with its environment. Decoherence suppresses off-diagonal density-matrix elements in a preferred basis.
Classical probability distribution: A function assigning probabilities to outcomes in a classical sample space. Both encode uncertainty, but density matrices also retain quantum coherence.
Quantum measurement: A physical interaction whose outcomes and probabilities are described by quantum theory. Measurement probabilities follow from the density matrix and the measurement operators.
Positive semidefinite matrix: A Hermitian matrix whose eigenvalues are all nonnegative. Positivity ensures density-matrix predictions assign no negative probabilities.

Linked from 17 pages