42,092 research outputs found
Quantum capacity of lossy channel with additive classical Gaussian noise : a perturbation approach
For a quantum channel of additive Gaussian noise with loss, in the general
case of copies input, we show that up to first order perturbation, any
non-Gaussian perturbation to the product thermal state input has a less quantum
information transmission rate when the input energy tend to infinitive.Comment: 4 page
Quantum capacity of channel with thermal noise
The quantum capacity of thermal noise channel is studied. The extremal input
state is obtained at the postulation that the coherent information is convex or
concave at its vicinity. When the input energy tends to infinitive, it is
verified by perturbation theory that the coherent information reaches its
maximum at the product of identical thermal state input. The quantum capacity
is obtained for lower noise channel and it is equal the one shot capacity.Comment: 5 page
Perfect A/D conversion of entanglement
We investigate how entanglement can be perfectly transfered between
continuous variable and qubits system. We find that a two-mode squeezed vacuum
state can be converted to the product state of an infinitive number of
two-qubit states while keeping the entanglement. The reverse process is also
possible. The interaction Hamitonian is a kind of non-linear Jaynes-Cumings
Hamiltonian.Comment: 3 pages, 1 figur
Gaussian relative entropy of entanglement
For two gaussian states with given correlation matrices, in order that
relative entropy between them is practically calculable, I in this paper
describe the ways of transforming the correlation matrix to matrix in the
exponential density operator. Gaussian relative entropy of entanglement is
proposed as the minimal relative entropy of the gaussian state with respect to
separable gaussian state set. I prove that gaussian relative entropy of
entanglement achieves when the separable gaussian state is at the border of
separable gaussian state set and inseparable gaussian state set. For two mode
gaussian states, the calculation of gaussian relative entropy of entanglement
is greatly simplified from searching for a matrix with 10 undetermined
parameters to 3 variables. The two mode gaussian states are classified as four
types, numerical evidence strongly suggests that gaussian relative entropy of
entanglement for each type is realized by the separable state within the same
type.For symmetric gaussian state it is strictly proved that it is achieved by
symmetric gaussian state.Comment: 12 pages, 3 figure
Locally inequivalent four qubit hypergraph states
Hypergraph states as real equally weighted pure states are important
resources for quantum codes of non-local stabilizer. Using local Pauli
equivalence and permutational symmetry, we reduce the 32768 four qubit real
equally weighted pure states to 28 locally inequivalent hypergraph states and
several graph states. The calculation of geometric entanglement supplemented
with entanglement entropy confirms that further reduction is impossible for
true hypergraph states.Comment: 6 pages,2 figures, Accepted by J. Phys.
On Graded Bialgebra Deformations
We introduce the graded bialgebra deformations, which explain
Andruskiewitsch-Schneider's liftings method. We also relate this graded
bialgebra deformation with the corresponding graded bialgebra cohomology
groups, which is the graded version of the one due to Gerstenhaber-Schack.Comment: Presented in AsiaLink Conference and Mistakes changed. To appear in
Alg. Coll
Entanglement of stabilizer codewords
The geometric measure, the logarithmic robustness and the relative entropy of
entanglement are proved to be equal for a stabilizer quantum codeword. The
entanglement upper and lower bounds are determined with the generators of code.
The entanglement of dual-containing CSS codes, Gottesman codes and the related
codes are given. An iterative algorithm is developed to determine the exact
value of the entanglement when the two bounds are not equal.Comment: 9 page
A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states
With a two step optimization method of entanglement witness, we analytically
propose a set of necessary and sufficient entanglement criteria for four qubit
symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set
contains four criteria. Two of them are linear with density matrix elements.
The other two criteria are nonlinear with density matrix elements. The
criterion set has a nest structure. A proper subset of the criteria is
necessary and sufficient for the entanglement of a proper subset of the states.
We illustrate the nest structure of criterion set with the general Werner state
set and its superset the highly symmetric GHZ diagonal state set, they are
subsets of the symmetric GHZ diagonal state set.Comment: 10 pages, 3 figure
Matched witness for multipartite entanglement
We transform the way of finding entanglement criterion into two steps: to
obtain necessary criterion of separability by maximizing an algebra function
for a set of characteristic variables of the witness operator and the given
number of partitions, then to obtain the sufficient criterion by minimizing an
algebra function with respect to the characteristic variables for a given
quantum state. Our method avoids the semi-definite program calculation in the
witness operator entanglement detection. The necessary and sufficient criterion
of separability for the three qubit X shaped state is given to illustrate the
procedure of finding the criterion. We give the necessary and sufficient
criteria of the three partite and full separabilities for the four qubit noisy
GHZ state and the four qubit noisy cluster state.Comment: 8 pages, no figure
The entanglement of some non-two-colorable graph states
We exactly evaluate the entanglement of a six vertex and a nine vertex graph
states which correspond to non ''two-colorable'' graphs. The upper bound of
entanglement for five vertices ring graph state is improved to 2.9275, less
than upper bound determined by LOCC. An upper bound of entanglement is proposed
based on the definition of graph state.Comment: 6 pages, 1 figur
- …