33 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.
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
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
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
Simulating extremal temporal correlations
The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or 'internal memory' of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections
Structure of temporal correlations of a qubit
In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of generalized measurements. We first characterize the polytope of temporal quantum correlations coming from the most general measurements. We then show that if the dimension of the quantum system is bounded, only a subset of the most general correlations can be realized and identify the correlations in the simplest scenario that can not be reached by two-dimensional systems. This leads to a temporal inequality for a dimension test, and we discuss a possible implementation using nitrogen-vacancy centers in diamond
Daemonic ergotropy: Generalised measurements and multipartite settings
Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical states
Maximal violation of state-independent contextuality inequalities
The discussion on noncontextual hidden variable models as an underlying description for the quantum-mechanical predictions started in ernest with 1967 paper by Kochen and Specker. There, it was shown that no noncontextual hidden-variable model can give these predictions. The proof used in that paper is complicated, but recently, a paper by Yu and Oh [PRL, 2012] proposes a simpler statistical proof that can also be the basis of an experimental test. Here we report on a sharper version of that statistical proof, and also explain why the algebraic upper bound to the expressions used are not reachable, even with a reasonable contextual hidden variable model. Specifically, we show that the quantum mechanical predictions reach the maximal possible value for a contextual model that keeps the expectation value of the measurement outcomes constant. © 2012 American Institute of Physics