Details
| Original language | English |
|---|---|
| Pages (from-to) | 062334 |
| Number of pages | 1 |
| Journal | Phys. Rev. A |
| Volume | 75 |
| Issue number | 6 |
| Publication status | Published - 2007 |
Abstract
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In: Phys. Rev. A, Vol. 75, No. 6, 2007, p. 062334.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A meaner king uses biased bases
AU - Reimpell, Michael
AU - Werner, Reinhard F.
PY - 2007
Y1 - 2007
N2 - The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell's original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.
AB - The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell's original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.
U2 - 10.1103/PhysRevA.75.062334
DO - 10.1103/PhysRevA.75.062334
M3 - Article
VL - 75
SP - 062334
JO - Phys. Rev. A
JF - Phys. Rev. A
SN - 2469-9934
IS - 6
ER -