|
| related topics |
| {measurement, state, measurements} |
| {states, state, optimal} |
| {information, entropy, channel} |
| {algorithm, log, probability} |
| {let, theorem, proof} |
| {photon, photons, single} |
| {error, code, errors} |
| {equation, function, exp} |
| {state, algorithm, problem} |
| {temperature, thermal, energy} |
| {state, states, entangled} |
| {key, protocol, security} |
| {vol, operators, histories} |
|
Quantum Detection with Unknown States
Noam Elron, Yonina C. Eldar
abstract: We address the problem of distinguishing among a finite collection of quantum
states, when the states are not entirely known. For completely specified
states, necessary and sufficient conditions on a quantum measurement minimizing
the probability of a detection error have been derived. In this work, we assume
that each of the states in our collection is a mixture of a known state and an
unknown state. We investigate two criteria for optimality. The first is
minimization of the worst-case probability of a detection error. For the second
we assume a probability distribution on the unknown states, and minimize of the
expected probability of a detection error.
We find that under both criteria, the optimal detectors are equivalent to the
optimal detectors of an ``effective ensemble''. In the worst-case, the
effective ensemble is comprised of the known states with altered prior
probabilities, and in the average case it is made up of altered states with the
original prior probabilities.
- oai_identifier:
- oai:arXiv.org:quant-ph/0501084
- categories:
- quant-ph
- comments:
- Refereed version. Improved numerical examples and figures. A few
typos fixed
- doi:
- 10.1103/PhysRevA.72.032338
- arxiv_id:
- quant-ph/0501084
- created:
- 2005-01-17
- updated:
- 2005-05-19
Full article ▸
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