Generalized Circulant Densities and a Sufficient Condition for Separability (2008)
Chruscinski, Dariusz, Pittenger, Arthur O.
In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpositrionm (PPT) property can be readily checked. These densities...
Classicality in discrete Wigner functions (2005)
Cormick, Cecilia, Galvao, Ernesto F., Gottesman, Daniel, Paz, Juan Pablo, Pittenger, Arthur O.
Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only...
Wigner Functions and Separability for Finite Systems (2005)
Pittenger, Arthur O., Rubin, Morton H.
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...
Mutually Unbiased Bases, Generalized Spin Matrices and Separability (2003)
Pittenger, Arthur O., Rubin, Morton H.
A collection of orthonormal bases for a complex dXd 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: ||...
Unextendible product bases and the construction of inseparable states (2002)
Let H[N] denote the tensor product of n finite dimensional Hilbert spaces H(r). A state |phi> of H[N] is separable if |phi> is the tensor product of states in the respective product spaces. An...
The geometry of entanglement witnesses and local detection of entanglement (2002)
Pittenger, Arthur O., Rubin, Morton H.
Let $H^{[ N]}=H^{[ d_{1}]}\otimes ... \otimes H^{[ d_{n}]}$ be a tensor product of Hilbert spaces and let $\tau_{0}$ be the closest separable state in the Hilbert-Schmidt norm to an entangled state...
Convexity and the Separability Problem of Quantum Mechanical Density Matrices (2001)
Pittenger, Arthur O., Rubin, Morton H.
A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate...
Note on Separability of the Werner states in arbitrary dimensions (2000)
Pittenger, Arthur O., Rubin, Morton H.
Great progress has been made recently in establishing conditions for separability of a particular class of Werner densities on the tensor product space of $n$ $d$--level systems (qudits). In this...
Separability and Fourier representations of density matrices (2000)
Pittenger, Arthur O., Rubin, Morton H.
Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$...
Complete Separability and Fourier representations of n-qubit states (1999)
Pittenger, Arthur O., Rubin, Morton H.
Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix...