# Ensemble

An ensemble of quantum states is a set of quantum states with corresponding probabilities. An ensemble E is written

E = {(pi, ρi)}
, where pi is the probability for the state ρi.

To each ensemble there is a corresponding average state

ρ̄ = ∑ipiρi
, 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.

Category: Quantum States