Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable
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Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable. / Clifton, Rob; Halvorson, Hans.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 61, No. 1, 012108, 01.2000, p. 12108-1-12108-5.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable
AU - Clifton, Rob
AU - Halvorson, Hans
PY - 2000/1
Y1 - 2000/1
N2 - Given a bipartite quantum system represented by a Hilbert space H1⊗H2, we give an elementary argument to show that if either dim H1 = ∞ or dim H2 = ∞, then the set of nonseparable density operators on H1⊗H2 is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when dim Hi<∝ for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.
AB - Given a bipartite quantum system represented by a Hilbert space H1⊗H2, we give an elementary argument to show that if either dim H1 = ∞ or dim H2 = ∞, then the set of nonseparable density operators on H1⊗H2 is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when dim Hi<∝ for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.
U2 - 10.1103/PhysRevA.61.012108
DO - 10.1103/PhysRevA.61.012108
M3 - Journal article
AN - SCOPUS:18844474297
VL - 61
SP - 12108-1-12108-5
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 1
M1 - 012108
ER -
ID: 336465277