Maximizing the Hilbert space for a finite number of distinguishable quantum states

Details Maximizing the Hilbert space for a finite number of distinguishable quantum states Maximizing the Hilbert space for a finite number of distinguishable quantum states

2003-04-06

arxiv.org/abs/quant-ph/0304050v1

Phys. Rev. Lett. 92, 097901 (2004), also appeared in Virtual Journal of Quantum Information, March 04 issue, and Virtual Journ

Physics

Quantum Physics

4 pages, 3 figures, submitted for publication

Scientific paper

10.1103/PhysRevLett.92.097901

We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number of qudits, then the Hilbert space dimension is maximized when each quantum particle is allowed to represent a qudit of order $e$. We demonstrate that the dimensionality of an entangled system, constrained by the total number quantum states, partitioned so as to maximize the number of qutrits will always exceed the dimensionality of other qudit partitioning. We then show that if we relax the requirement of partitioning the system into qudits, but instead let the particles exist in any given state, that the Hilbert space dimension is greatly increased.

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