General theory of measurement with two copies of a quantum state

Bendersky, Ariel; Paz, Juan Pablo; Cunha, Marcelo Terra

General theory of measurement with two copies of a quantum state

Authors

Bendersky, Ariel

Paz, Juan Pablo

Cunha, Marcelo Terra

Description

We analyze the possible results of the most general measurement on two copies of a quantum state. We show that $μ$ can label a set of outcomes of such measurement if and only if there is a family of completely co--positive (ccP) maps $C_μ$ such that the probability of occurrence $Prob(μ)$ is the fidelity of the map $C_μ$, i.e. $Prob(μ)= Tr(ρC_μ(ρ))$ which 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 ccPMVM). We present examples of ccPMVM's and discuss their tomographic applications showing that two copies of a state provide an exponential improvement in the efficiency of quantum state tomography. This enables the existence of an efficient universal detector.
4 pages, 1 figure