Entanglement of formation for a class of (2⊗d)(2\otimes d)-dimensional systems

Currently the entanglement of formation can be calculated analytically for mixed states in a $(2\otimes2)$-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 ($2\otimes d$)-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 $^1S_0$ 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 $\sim \verb+70$. In particular, for the KVI experiment the violation of the CHSH-Bell inequality should be corrected by a factor $\sim\verb+10$ from the pure $^1S_0$ 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 $\equiv$ \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

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

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