Generalized measurement postulate

A generalized quantum measurement is specified by operators

M_{i}

satisfying

\sum_{i} M_{i}^{†} M_{i} = I

. On input

ρ

, outcome

i

has probability

Tr (M_{i}^{†} M_{i} ρ)

and conditional state

M_{i} ρ M_{i}^{†} / Tr (M_{i}^{†} M_{i} ρ)

.

Table of contents
- Positive operator-valued measure Generalized measurement postulate

Positive operator-valued measure (POVM)

A positive operator-valued measure is a family of positive operators

E_{i}

satisfying

\sum_{i} E_{i} = I

. It determines measurement probabilities

Pr (i) = Tr (E_{i} ρ)

; choosing measurement operators with

E_{i} = M_{i}^{†} M_{i}

additionally determines state updates.

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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 323 / 5 / a / i / Solution

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