Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 325 / 1 / a

Table of contents
- Solution a

Solution

For a bipartite density operator

ρ_{S A}

, the reduced density matrix of

S

is

ρ_{S} = Tr_{A} ρ_{S A} .

It is characterized by

Tr_{S} (M_{S} ρ_{S}) = Tr_{S A} [(M_{S} \otimes I_{A}) ρ_{S A}]

for every observable

M_{S}

on

S

. Equivalently, in any orthonormal basis

{∣ a_{k} ⟩}

of

A

, the partial trace is

ρ_{S} = \sum_{k} (I_{S} \otimes ⟨ a_{k} ∣) ρ_{S A} (I_{S} \otimes ∣ a_{k} ⟩),

and the result is independent of that basis.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version