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Abstract A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension pn where p is a prime number. With this limitation it is possible to define a phase space and Wigner… (More)

A finite dimensional quantum mechanical system is modeled by a density ρ, a trace one, positive semi-definite matrix on a suitable tensor product space H . For the system to demonstrate experimentally certain non-classical behavior, ρ cannot be in S, a closed convex set of densities whose extreme points have a specificed tensor product form. Two… (More)

A collection of orthonormal bases for a d × d Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |〈v, w〉|2 = 1 d . The MUB problem is to prove or disprove the the existence of a maximal set of d+1 bases. It has been shown in [W. K. Wootters, B. D. Fields, Annals of… (More)

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for ddimensional spaces, and the resulting set of unitary matrices S (d) is a basis for d × d matrices. If N = d1 × d2 × · · · × db and H [N] = ⊗ H k, we give a sufficient condition for separability of a density matrix ρ relative to the H [dk] in terms of the L1 norm of… (More)

In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transposition (PPT) property can be readily checked. These densities were also investigated from a different perspective by Baumgartner, Hiesmayr and Narnhofer. In this paper we show how the support of such densities can be expressed… (More)

- A. O. Pittenger
- Math. Oper. Res.
- 1988

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