769 research outputs found
Complete Separability and Fourier representations of n-qubit states
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 to define the
relationship between these two bases and to emphasize its interpretation as a
Fourier transform. We then prove a general sufficient condition for complete
separability in terms of the spin coefficients and give necessary and
sufficient conditions for the complete separability of a class of generalized
Werner densities. As a further application of the theory, we give necessary and
sufficient conditions for full separability for a particular set of -qubit
states whose densities all satisfy the Peres condition
Mutually Unbiased Bases, Generalized Spin Matrices and Separability
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: || ^{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 Physics, 191, no. 2, 363-381,
(1989)] that such a collection exists if d is a power of a prime number p. We
revisit this problem and use dX d generalizations of the Pauli spin matrices to
give a constructive proof of this result. Specifically we give explicit
representations of commuting families of unitary matrices whose eigenvectors
solve the MUB problem. Additionally we give formulas from which the orthogonal
bases can be readily computed. We show how the techniques developed here
provide a natural way to analyze the separability of the bases. The techniques
used require properties of algebraic field extensions, and the relevant part of
that theory is included in an Appendix
Quantum Mechanics of a Two Photon State
We review the formalism for describing the two photon state produced in spontaneous parametric down conversion
Effects of mismatched transmissions on two-mode squeezing and EPR correlations with a slow light medium
We theoretically discuss the preservation of squeezing and continuous
variable entanglement of two mode squeezed light when the two modes are
subjected to unequal transmission. One of the modes is transmitted through a
slow light medium while the other is sent through an optical fiber of unit
transmission. Balanced homodyne detection is used to check the presence of
squeezing. It is found that loss of squeezing occurs when the mismatch in the
transmission of the two modes is greater than 40% while near ideal squeezing is
preserved when the transmissions are equal. We also discuss the effect of this
loss on continuous variable entanglement using strong and weak EPR criteria and
possible applications for this experimental scheme.Comment: 7 pages, 4 figure
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