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Ensemble

An ensemble of quantum states is a set of quantum states with corresponding probabilities. An ensemble $\mathcal{E}$ is written

$\mathcal{E} = \{ (p_i, \rho_i) \}$ ,

where $p i$ is the probability for the state $ρ i$ .

To each ensemble there is a corresponding average state

$\bar{\rho} = \sum_i p_i \rho_i$ ,

but any mixed state can be realized by many different ensembles, even if the states in the states in the ensemble are restricted to pure states.

Usage

For sending classical information over quantum channels, one has to choose an ensemble of states to encode the information. The maximum information which is possible to transmit with a given ensemble is called the accessible information.
A (non-destructive) measurement on a quantum state will define an ensemble of post-measurement states. If the measurement outcome is discarded, the state will be in the average state.
Different ensembles of pure states is used to define the entanglement of formation.