Remote information concentration and multipartite entanglement in multilevel systems

Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found, i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.Comment: 10 pages, 3 figure

Genuinely multipartite entangled states and orthogonal arrays

A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, written k-uniform, if all its reductions to k qudits are maximally mixed. These states form a natural generalization of N-qudits GHZ states which belong to the class 1-uniform states. We establish a link between the combinatorial notion of orthogonal arrays and k-uniform states and prove the existence of several new classes of such states for N-qudit systems. In particular, known Hadamard matrices allow us to explicitly construct 2-uniform states for an arbitrary number of N>5 qubits. We show that finding a different class of 2-uniform states would imply the Hadamard conjecture, so the full classification of 2-uniform states seems to be currently out of reach. Additionally, single vectors of another class of 2-uniform states are one-to-one related to maximal sets of mutually unbiased bases. Furthermore, we establish links between existence of k-uniform states, classical and quantum error correction codes and provide a novel graph representation for such states.Comment: 24 pages, 7 figures. Comments are very welcome

Detecting Full N-Particle Entanglement in Arbitrarily High-Dimensional Systems with Bell-Type Inequality

We derive a set of Bell-type inequalities for arbitrarily high-dimensional systems, based on the assumption of partial separability in the hybrid local-nonlocal hidden variable model. Partially entangled states would not violate the inequalities, and thus upon violation, these Bell-type inequalities are sufficient conditions to detect the full $N$-particle entanglement and validity of the hybrid local-nonlocal hidden variable description.Comment: 6 page

QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB

A program package for MATLAB is introduced that helps calculations in quantum information science and quantum optics. It has commands for the following operations: (i) Reordering the qudits of a quantum register, computing the reduced state of a quantum register. (ii) Defining important quantum states easily. (iii) Formatted input and output for quantum states and operators. (iv) Constructing operators acting on given qudits of a quantum register and constructing spin chain Hamiltonians. (v) Partial transposition, matrix realignment and other operations related to the detection of quantum entanglement. (vi) Generating random state vectors, random density matrices and random unitaries.Comment: 22 pages, no figures; small changes, published versio

Security bound of two-bases quantum key-distribution protocols using qudits

We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.Comment: 12 pages, 2 figures, to appear in Phys. Rev.

Entanglement sharing: from qubits to Gaussian states

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such 'monogamy constraints' have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In these proceedings we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.Comment: 11 pages. Proceedings of the workshop "Entanglement in physical and information sciences", Centro Ennio de Giorgi, Pisa, December 2004. (v2) References updated, final version published in Int. J. Quant. In

Versatile shaper-assisted discretization of energy-time entangled photons

We demonstrate the capability to discretize the frequency spectrum of broadband energy-time entangled photons by means of a spatial light modulator to encode qudits in various bases. Exemplarily, we implement three different discretization schemes, namely frequency bins, time bins and Schmidt modes. Entangled qudits up to dimension $d=4$ are then revealed by two-photon interference experiments with visibilities violating a $d$-dimensional Bell inequality.Comment: 22 pages, 11 figure