42 research outputs found
Entanglement of formation for a class of -dimensional systems
Currently the entanglement of formation can be calculated analytically for
mixed states in a -dimensional Hilbert space. For states in higher
dimensional Hilbert space a closed formula for quantifying entanglement does
not exist. In this regard only entanglement bounds has been found for
estimating it. In this work, we find an analytical expression for evaluating
the entanglement of formation for bipartite ()-dimensional mixed
states.Comment: 5 pages, 4 figures. Submitted for publicatio
Effect of the unpolarized spin state in spin-correlation measurement of two protons produced in the 12C(d,2He) reaction
In this note we discuss the effect of the unpolarized state in the
spin-correlation measurement of the two-proton state produced in
12C(d,2He) reaction at the KVI, Groningen. We show that in the presence of the
unpolarized state the maximal violation of the CHSH-Bell inequality is lower
than the classical limit if the purity of the state is less than . In particular, for the KVI experiment the violation of the
CHSH-Bell inequality should be corrected by a factor from the
pure state.Comment: 6 pages, to appear in J. Phys.
Quantum measurement incompatibility in subspaces
We consider the question of characterizing the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility-measurements that become compatible in every subspace, (ii) fully compressible incompatibility-measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility-measurements that are compatible in some subspace and incompatible in another. For each class, we discuss explicit examples. Finally, we present some applications of these ideas. First, we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second, we highlight the implications of our results for tests of quantum steering
Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction
We have studied occurrence of quantum phase transition in the one-dimensional
spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi-
partite and multi-partite entanglement point of view. Using exact numerical
solutions, we are able to study such systems up to 24 qubits. The minimum of
the entanglement ratio R \tau 2/\tau 1 < 1, as a novel estimator of
QPT, has been used to detect QPT and our calculations have shown that its
minimum took place at the critical point. We have also shown both the
global-entanglement (GE) and multipartite entanglement (ME) are maximal at the
critical point for the Ising chain with added DM interaction. Using matrix
product state approach, we have calculated the tangle and concurrence of the
model and it is able to capture and confirm our numerical experiment result.
Lack of inversion symmetry in the presence of DM interaction stimulated us to
study entanglement of three qubits in symmetric and antisymmetric way which
brings some surprising results.Comment: 18 pages, 9 figures, submitte
D-concurrence bounds for pair coherent states
The pair coherent state is a state of a two-mode radiation field which is
known as a state with non-Gaussian wave function. In this paper, the upper and
lower bounds for D-concurrence (a new entanglement measure) have been studied
over this state and calculated.Comment: 11 page
Additivity and non-additivity of multipartite entanglement measures
We study the additivity property of three multipartite entanglement measures,
i.e. the geometric measure of entanglement (GM), the relative entropy of
entanglement and the logarithmic global robustness. First, we show the
additivity of GM of multipartite states with real and non-negative entries in
the computational basis. Many states of experimental and theoretical interests
have this property, e.g. Bell diagonal states, maximally correlated generalized
Bell diagonal states, generalized Dicke states, the Smolin state, and the
generalization of D\"{u}r's multipartite bound entangled states. We also prove
the additivity of other two measures for some of these examples. Second, we
show the non-additivity of GM of all antisymmetric states of three or more
parties, and provide a unified explanation of the non-additivity of the three
measures of the antisymmetric projector states. In particular, we derive
analytical formulae of the three measures of one copy and two copies of the
antisymmetric projector states respectively. Third, we show, with a statistical
approach, that almost all multipartite pure states with sufficiently large
number of parties are nearly maximally entangled with respect to GM and
relative entropy of entanglement. However, their GM is not strong additive;
what's more surprising, for generic pure states with real entries in the
computational basis, GM of one copy and two copies, respectively, are almost
equal. Hence, more states may be suitable for universal quantum computation, if
measurements can be performed on two copies of the resource states. We also
show that almost all multipartite pure states cannot be produced reversibly
with the combination multipartite GHZ states under asymptotic LOCC, unless
relative entropy of entanglement is non-additive for generic multipartite pure
states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by
correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published
version. The abstract, introduction, and summary are also revised. All other
conclusions are unchange
Inferring superposition and entanglement from measurements in a single basis
We discuss what can be inferred from measurements on one- and two-qubit
systems using a single measurement basis at various times. We show that, given
reasonable physical assumptions, carrying out such measurements at
quarter-period intervals is enough to demonstrate coherent oscillations of one
or two qubits between the relevant measurement basis states. One can thus infer
from such measurements alone that an approximately equal superposition of two
measurement basis states has been created in a coherent oscillation experiment.
Similarly, one can infer that a near maximally entangled state of two qubits
has been created in an experiment involving a putative SWAP gate. These results
apply even if the relevant quantum systems are only approximate qubits. We
discuss applications to fundamental quantum physics experiments and quantum
information processing investigations.Comment: Final published versio