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 -