# nLab positive-operator-valued measure

Contents

### Context

#### Measure and probability theory

measure theory

probability theory

# Contents

## Idea

Given a measurable space $X$ and a Hilbert space $H$, then a positive-operator–valued measure (POVM) is essentially a probability measure on $X$ with values in the positive operators on $H$.

Any such induces a quantum operation and these are precisely the quantum operations which encode quantum measurement.

## References

Last revised on October 1, 2014 at 06:35:38. See the history of this page for a list of all contributions to it.