Quantum Computation and the Separability Problem
Arthur Pittenger
Dept. of Mathematics and Statistics, UMBC
Wednesday, April 24, 2002 15:00-16:00,
Room 145, NIST North (820)
Gaithersburg
Wednesday, April 24, 2002 13:00-14:00,
Room 4511
Boulder
Abstract:
If information is stored at the level of a single particle, one
has to use quantum mechanics to analyze the physics of the storage system
and the "programming" of algorithms. In this talk we briefly review the
pre-history of quantum computation and describe the mathematics one needs
for quantum algorithms. In particular, if several systems are involved,
tensor products of spaces are a key part of the structure. We illustrate
the role of different quantum systems in subroutines which could be used
in algorithms.
Tensor product spaces provide the language and context for
defining when several systems are "entangled" or when they are separable.
One can pose this "separability problem" in terms of nested compact convex
sets in a real Hilbert space of very high dimension. This gives a
geometric context which unifies some recent research on the separability
problem.
Contact: A. J. KearsleyNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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