An expectation value expansion of Hermitian operators in a discrete Hilbert space

Details An expectation value expansion of Hermitian operators in a discrete Hilbert space An expectation value expansion of Hermitian operators in a discrete Hilbert space

2000-11-09

arxiv.org/abs/quant-ph/0011037v2

Physics

Quantum Physics

A mild update. In particular, I. D. Ivanovic's earlier derivation of the expansion is properly acknowledged. 16 pages, one PS

Scientific paper

10.1088/1464-4266/3/3/314

We discuss a real-valued expansion of any Hermitian operator defined in a Hilbert space of finite dimension N, where N is a prime number, or an integer power of a prime. The expansion has a direct interpretation in terms of the operator expectation values for a set of complementary bases. The expansion can be said to be the complement of the discrete Wigner function. We expect the expansion to be of use in quantum information applications since qubits typically are represented by a discrete, and finite-dimensional physical system of dimension N=2^p, where p is the number of qubits involved. As a particular example we use the expansion to prove that an intermediate measurement basis (a Breidbart basis) cannot be found if the Hilbert space dimension is 3 or 4.

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