22 research outputs found
Multiaccess quantum communication and product higher rank numerical range
In the present paper we initiate the study of the product higher rank
numerical range. The latter, being a variant of the higher rank numerical range
[M.--D. Choi {\it et al.}, Rep. Math. Phys. {\bf 58}, 77 (2006); Lin. Alg.
Appl. {\bf 418}, 828 (2006)], is a natural tool for studying construction of
quantum error correction codes for multiple access channels. We review
properties of this set and relate it to other numerical ranges, which were
recently introduced in the literature. Further, the concept is applied to the
construction of codes for bi--unitary two--access channels with a hermitian
noise model. Analytical techniques for both outerbounding the product higher
rank numerical range and determining its exact shape are developed for this
case. Finally, the reverse problem of constructing a noise model for a given
product range is considered.Comment: 26 pages, 6 figure
Reexamination of determinant-based separability test for two qubits
It was shown in [Augusiak et al.,\;Phys. Rev. A \textbf{77}, 030301(R)
(2008)] that discrimination between entanglement and separability in a two
qubit state can be achieved by a measurement of a single observable on four
copies of it. Moreover, a pseudo entanglement monotone was proposed to
quantify entanglement in such states. The main goal of the present paper is to
show that close relationship between and concurrence reported there is a
result of sharing the same underlying construction of a spin flipped matrix. We
also show that monogamy of entanglement can be rephrased in terms of and
prove the factorization law for .Comment: improved v3, journal ref. adde
General construction of noiseless networks detecting entanglement with help of linear maps
We present the general scheme for construction of noiseless networks
detecting entanglement with the help of linear, hermiticity-preserving maps. We
show how to apply the method to detect entanglement of unknown state without
its prior reconstruction. In particular, we prove there always exists noiseless
network detecting entanglement with the help of positive, but not completely
positive maps. Then the generalization of the method to the case of
entanglement detection with arbitrary, not necessarily hermiticity-preserving,
linear contractions on product states is presented.Comment: Revtex, 6 pages, 3 figures, published versio
Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
Einstein-Podolsky-Rosen steering is a form of inseparability in quantum
theory commonly acknowledged to be intermediate between entanglement and Bell
nonlocality. However, this statement has so far only been proven for a
restricted class of measurements, namely projective measurements. Here we prove
that entanglement, one-way steering, two-way steering and nonlocality are
genuinely different considering general measurements, i.e. single round
positive-operator-valued-measures. Finally, we show that the use of sequences
of measurements is relevant for steering tests, as they can be used to reveal
"hidden steering".Comment: Typo in equation 13 corrected (noticed by Jessica Bavaresco