Details
| Original language | English |
|---|---|
| Pages (from-to) | 62-75 |
| Number of pages | 14 |
| Journal | J. Math. Phys. |
| Volume | 36 |
| Issue number | 1 |
| Publication status | Published - 1995 |
Abstract
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In: J. Math. Phys., Vol. 36, No. 1, 1995, p. 62-75.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mixed states with positive Wigner functions
AU - Bröcker, T.
AU - Werner, R. F.
PY - 1995
Y1 - 1995
N2 - According to a result of Hudson, the Wigner distribution function of a pure quantum state is everywhere positive if and only if the state is coherent. The characterization of mixed states with positive Wigner function is a special case of the problem of determining functions satisfying a twisted positive definiteness condition for a prescribed set of twisting parameters (i.e. functions with given Wigner spectrum in the sense of Narcowich). If a state is a convex combination of coherent states, it has the property that the Wigner spectrum contains the unit interval, which in turn implies that the Wigner function is positive. We show by explicit examples that the converses of both implications are false. The examples are taken from a low dimensional section of the state space, in which all Wigner spectra can be computed. In this set we also find counterexamples to a conjecture by Narcowich concerning the Wigner spectrum of products, as well as a state whose Wigner spectrum is a convergent sequence of discrete points.
AB - According to a result of Hudson, the Wigner distribution function of a pure quantum state is everywhere positive if and only if the state is coherent. The characterization of mixed states with positive Wigner function is a special case of the problem of determining functions satisfying a twisted positive definiteness condition for a prescribed set of twisting parameters (i.e. functions with given Wigner spectrum in the sense of Narcowich). If a state is a convex combination of coherent states, it has the property that the Wigner spectrum contains the unit interval, which in turn implies that the Wigner function is positive. We show by explicit examples that the converses of both implications are false. The examples are taken from a low dimensional section of the state space, in which all Wigner spectra can be computed. In this set we also find counterexamples to a conjecture by Narcowich concerning the Wigner spectrum of products, as well as a state whose Wigner spectrum is a convergent sequence of discrete points.
U2 - 10.1063/1.531326
DO - 10.1063/1.531326
M3 - Article
VL - 36
SP - 62
EP - 75
JO - J. Math. Phys.
JF - J. Math. Phys.
SN - 1089-7658
IS - 1
ER -