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Register a new userVerifying bound entanglement of dephased Werner states
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The verification of quantum entanglement under the influence of realistic noise and decoherence is crucial for the development of quantum technologies. Unfortunately, a full entanglement characterization is generally not possible with most entanglement criteria such as entanglement witnesses or the partial transposition criterion. In particular, so called bound entanglement cannot be certified via the partial transposition criterion. Here we present the full entanglement verification of dephased qubit and qutrit Werner states via entanglement quasiprobabilities. Remarkably, we are able to reveal bound entanglement for noisy-mixed states in the qutrit case. This example demonstrates the strength of the entanglement quasiprobabilities for verifying the full entanglement of quantum states suffering from noise.
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We address the presence of bound entanglement in strongly-interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the systems size. Specific examples for one- and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.
The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally complete positive operator-valued measure (SIC-POVM) in the Hilbert space. We successfully get the decomposition for arbitrary $Ntimes N$ Werner state in terms of regular simplexes. Meanwhile, the decomposition of isotropic state is found to be related to the decomposition of Werner state via partial transposition. It is interesting to note that in the large $N$ limit, while the Werner states are either separable or non-steerably entangled, most of the isotropic states tend to be steerable.
An algorithm is proposed that serves to handle full rank density matrices, when coming from a lower rank method to compute the convex-roof. This is in order to calculate an upper bound for any polynomial SL invariant multipartite entanglement measure E. Here, it is exemplifyed how this algorithm works, based on a method for calculating convex-roofs of rank two density matrices. It iteratively considers the decompositions of the density matrix into two states each, exploiting the knowledge for the rank-two case. The algorithm is therefore quasi exact as far as the two rank case is concerned, and it also gives hints where it should include more states in the decomposition of the density matrix. Focusing on the threetangle, I show the results the algorithm gives for two states, one of which being the $GHZ$-Werner state, for which the exact convex roof is known. It overestimates the threetangle in the state, thereby giving insight into the optimal decomposition the $GHZ$-Werner state has. As a proof of principle, I have run the algorithm for the threetangle on the transverse quantum Ising model. I give qualitative and quantitative arguments why the convex roof should be close to the upper bound found here.
We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures obtaining exact analytical results in special instances, and upper and lower bounds in the general case. Non-Gaussian measurements such as photon counting are in general necessary to solve the optimization in the definition of quantum discord, whereas Gaussian measurements are strictly suboptimal for the considered states. The gap between Gaussian and optimal non-Gaussian conditional entropy is found to be proportional to a measure of non-Gaussianity in the regime of low squeezing, for a subclass of continuous-variable Werner states. We further study an example of a non-Gaussian state which is positive under partial transposition, and whose nonclassical correlations stay finite and small even for infinite squeezing. Our results pave the way to a systematic exploration of the interplay between nonclassicality and non-Gaussianity in continuous-variable systems, in order to gain a deeper understanding of -and to draw a bigger advantage from- these two important resources for quantum technology.
We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner state $rho = v |psi_- > <psi_- | + (1- v ) frac{1}{4}$ via a local hidden variable (LHV) model, where $|psi_- >$ denotes the singlet state. We show analytically that these correlations are local for $ v = 999times689times{10^{-6}}$ $cos^4(pi/50) simeq 0.6829$. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constant $K_G(3) leq 1/v simeq 1.4644$. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state for $v simeq 0.4553$. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.
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