General theory of measurement with two copies of a quantum state

ARIEL BENDERSKY; MARCELO TERRA CUNHA; JUAN PABLO PAZ

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Año: 2009 vol. 103 p. 40404 - 40405

0031-9007

We analyze the results of the most general measurement on two copies of a quantum state. By doing that, we show that two copies of a quantum state enable the construction of an efficient universal state tomographer. We demonstrate that $mu$ can label a set of outcomes of a measurement on two Copies if and only if there is a family maps $C_mu$ such that the probability $Prob(mu)$ is the fidelity of the map, i.e. $Prob(mu)= Tr( ho C_mu( ho))$. Here, the map $C_mu$ must be completely positive after being composed with the transposition (these are called completely co-positive, or ccP, maps) and must add up to the fully depolarizing map. This implies that a POVM on two copies induces a measure on the set of ccP maps (i.e., a ccP Map Valued Measure, or ccPMVM).