|
| related topics |
| {states, state, optimal} |
| {let, theorem, proof} |
| {measurement, state, measurements} |
| {error, code, errors} |
| {information, entropy, channel} |
| {group, space, representation} |
| {alice, bob, state} |
| {photon, photons, single} |
| {vol, operators, histories} |
|
On Quantum Detection and the Square-Root Measurement
Yonina C. Eldar, G. David Forney
abstract: In this paper we consider the problem of constructing measurements optimized
to distinguish between a collection of possibly non-orthogonal quantum states.
We consider a collection of pure states and seek a positive operator-valued
measure (POVM) consisting of rank-one operators with measurement vectors
closest in squared norm to the given states. We compare our results to previous
measurements suggested by Peres and Wootters [Phys. Rev. Lett. 66, 1119 (1991)]
and Hausladen et al. [Phys. Rev. A 54, 1869 (1996)], where we refer to the
latter as the square-root measurement (SRM). We obtain a new characterization
of the SRM, and prove that it is optimal in a least-squares sense. In addition,
we show that for a geometrically uniform state set the SRM minimizes the
probability of a detection error. This generalizes a similar result of Ban et
al. [Int. J. Theor. Phys. 36, 1269 (1997)].
- oai_identifier:
- oai:arXiv.org:quant-ph/0005132
- categories:
- quant-ph
- comments:
- Version of August 29, 2000, with minor revisions. To appear in the
IEEE Transactions on Information Theory. RevTex, 48 pages, 3 figures. A
briefer version of this paper has also been submitted to Physical Review
Letters. A copy is obtainable by writing to the authors at yonina@mit.edu
- arxiv_id:
- quant-ph/0005132
- journal_ref:
- IEEE Trans. Inform. Theory, vol. 47, pp. 858-872, Mar. 2001
- created:
- 2000-05-31
- updated:
- 2000-08-29
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