Abstract
We analyse the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such. comparisons without obtaining any information about the individual transformations. Different comparison strategies are presented and compared with respect to their efficiency. With an interferometric setup, it is possible to compare two unitary transforms using only one test particle. Another strategy makes use of a two-particle singlet state. This strategy is more efficient than using a non-entangled two-particle test state, thus demonstrating the benefit of entanglement. Generalizations to higher.-dimensional transforms and to more than two transformations are made.
| Original language | English |
|---|---|
| Pages (from-to) | 2325-2338 |
| Number of pages | 14 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 36 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 7 Mar 2003 |
Cite this
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Comparison of unitary transforms. / Andersson, Anna Erika Elisabeth; Jex, Igor; Barnett, Stephen M.
In: Journal of Physics A: Mathematical and General, Vol. 36, No. 9, 07.03.2003, p. 2325-2338.Research output: Contribution to journal › Article
TY - JOUR
T1 - Comparison of unitary transforms
AU - Andersson, Anna Erika Elisabeth
AU - Jex, Igor
AU - Barnett, Stephen M
PY - 2003/3/7
Y1 - 2003/3/7
N2 - We analyse the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such. comparisons without obtaining any information about the individual transformations. Different comparison strategies are presented and compared with respect to their efficiency. With an interferometric setup, it is possible to compare two unitary transforms using only one test particle. Another strategy makes use of a two-particle singlet state. This strategy is more efficient than using a non-entangled two-particle test state, thus demonstrating the benefit of entanglement. Generalizations to higher.-dimensional transforms and to more than two transformations are made.
AB - We analyse the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such. comparisons without obtaining any information about the individual transformations. Different comparison strategies are presented and compared with respect to their efficiency. With an interferometric setup, it is possible to compare two unitary transforms using only one test particle. Another strategy makes use of a two-particle singlet state. This strategy is more efficient than using a non-entangled two-particle test state, thus demonstrating the benefit of entanglement. Generalizations to higher.-dimensional transforms and to more than two transformations are made.
U2 - 10.1088/0305-4470/36/9/310
DO - 10.1088/0305-4470/36/9/310
M3 - Article
VL - 36
SP - 2325
EP - 2338
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
SN - 0305-4470
IS - 9
ER -