361 research outputs found
Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
Quantum entanglement plays crucial roles in quantum information processing.
Quantum entangled states have become the key ingredient in the rapidly
expanding field of quantum information science. Although the nonclassical
nature of entanglement has been recognized for many years, considerable efforts
have been taken to understand and characterize its properties recently. In this
review, we introduce some recent results in the theory of quantum entanglement.
In particular separability criteria based on the Bloch representation,
covariance matrix, normal form and entanglement witness; lower bounds,
subadditivity property of concurrence and tangle; fully entangled fraction
related to the optimal fidelity of quantum teleportation and entanglement
distillation will be discussed in detail.Comment: 63 pages, 4 figure
A note on the Bloch representation of absolutely maximally entangled states
The absolutely maximally entangled (AME) states play key roles in quantum
information processing. We provide an explicit expression of the generalized
Bloch representation of AME states for general dimension of individual
subsystems and arbitrary number of partite . Based on this analytic formula,
we prove that the trace of the squared support for any given weight is given by
the so-called hyper-geometric function and is irrelevant with the choices of
the subsystems. The optimal point for the existence of AME states is obtained
Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order
We investigate the eigenvalues of the buckling problem of arbitrary order on
compact domains in Euclidean spaces and spheres. We obtain universal bounds for
the th eigenvalue in terms of the lower eigenvalues independently of the
particular geometry of the domain.Comment: 24 page
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