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arXiv · 0904.3576

General theory of measurement with two copies of a quantum state

Ariel Bendersky·Juan Pablo Paz·Marcelo Terra Cunha
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Abstract

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.

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Ariel Bendersky, Juan Pablo Paz, Marcelo Terra Cunha. 2009-04-22. General theory of measurement with two copies of a quantum state. https://arxiv.org/abs/0904.3576

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