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

E = {(*p**i*, *ρ**i*)}, where *p**i* is the probability for the state *ρ**i*.

To each ensemble there is a corresponding *average state*

*ρ̄* = ∑*i**p**i**ρ**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.

## Last modified:

Monday, October 26, 2015 - 17:56