Entanglement Generation from Thermal Spin States via Unitary Beam Splitters

We suggest a method of generating distillable entanglement form mixed states unitarily, by utilizing the flexibility of dimension od occupied Hilbert space. We present a model of a thermal spin state entering a beam splitter generating entanglement. It is the truncation of the state that allows for entanglement generation. The output entanglement is investigated for different temperatures and it is found that more randomness - in the form of higher temperature - is better for this set up.Comment: 4 pages, 3 figures. Small changes in accordance with journal advice to make more readable. Improved discussion on implemetability of scheme, and references adde

Classicality of Spin Coherent States via Entanglement and Distinguishability

We investigate the classical nature of the spin coherent states. In addition to being minimum uncertainty states, as the size of the spin, S, increases, the classical nature is seen to increase in two respects: in their resistance to entanglement generation (when passed through a beam splitter) and in the distinguishability of the states. In the infinite S limit the spin coherent state is a subclass of the optical coherent states (namely the subclass of orthogonal optical coherent states). These states generate no entanglement and are obviously completely distinguishable. The decline of the generated entanglement, and in this sense increase in classicality with S, is very slow and dependent on the amplitude z of the state. Surprisingly we find that for |z| > 1 there is an initial increase in entanglement followed by an extremely gradual decline to zero. The distinguishability, on the other hand, quickly becomes classical for all z. We illustrate the distinguishability of spin coherent states in a novel manner using the representation of Majorana

Survival of entanglement in thermal states

We present a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground state entanglement. The condition is written in terms of the ground state entanglement and the partition function and it gives transition temperatures below which entanglement is guaranteed to survive. It is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Examples where the condition is calculated are given. These examples allow us to characterize a minimum gapping behavior for the survival of entanglement in the thermodynamic limit. Further, the same technique can be used to find noise thresholds in the generation of useful resource states for one-way quantum computing.Comment: 6 pages, 2 figures. Changes made in line with publication recommendations. Motivation and concequences of result clarified, with the addition of one more example, which applies the result to give noise thresholds for measurement based quantum computing. New author added with new result

Which graph states are useful for quantum information processing?

Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterisation of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general kinds of MBQC: uniform equiprobability and constant probability. These classes can be useful from a cryptographic and information point of view because even though we cannot do a deterministic computation in general we can preserve the information and transfer it perfectly from the inputs to the outputs. We derive simple graph characterisations for these classes and prove that the deterministic and uniform equiprobability classes collapse when the cardinalities of inputs and outputs are the same. We also prove the reversibility of gflow in that case. The new graphical characterisations allow us to go from open graphs to graphs in general and to consider this question: given a graph with no inputs or outputs fixed, which vertices can be chosen as input and output for quantum information processing? We present a characterisation of the sets of possible inputs and ouputs for the equiprobability class, which is also valid for deterministic computations with inputs and ouputs of the same cardinality.Comment: 13 pages, 2 figure

Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light

Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings

Integrated Diamond Optics for Single Photon Detection

Optical detection of single defect centers in the solid state is a key element of novel quantum technologies. This includes the generation of single photons and quantum information processing. Unfortunately the brightness of such atomic emitters is limited. Therefore we experimentally demonstrate a novel and simple approach that uses off-the-shelf optical elements. The key component is a solid immersion lens made of diamond, the host material for single color centers. We improve the excitation and detection of single emitters by one order of magnitude, as predicted by theory.Comment: 10 pages, 3 figure

Direct evaluation of pure graph state entanglement

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory, namely the identification of maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore we show that computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by explicit construction of closest separable and closest product states respectively. We show how these separable states can be described using stabiliser formalism as well as PEPs-like construction. Finally we discuss the way in which introducing noise to the system can optimally destroy entanglement.Comment: 23 pages, 9 figure

Entanglement in pure and thermal cluster states

We present a closest separable state to cluster states. We start by considering linear cluster chains and extend our method to cluster states that can be used as a universal resource in quantum computation. We reproduce known results for pure cluster states and show how our method can be used in quantifying entanglement in noisy cluster states. Operational meaning is given to our method that clearly demonstrates how these closest separable states can be constructed from two-qubit clusters in the case of pure states. We also discuss the issue of finding the critical temperature at which the cluster state becomes only classically correlated and the importance of this temperature to our method.Comment: Revised extended version, references added. 14 pages, 4 figure

Generating topological order from a 2D cluster state using a duality mapping

In this paper we prove, extend and review possible mappings between the two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and Kitaev's toric code model. We introduce a two-dimensional duality transformation to map the two-dimensional lattice cluster state into the topologically-ordered Wen model. Then, we subsequently investigates how this mapping could be achieved physically, which allows us to discuss the rate at which a topologically ordered system can be achieved. Next, using a lattice fermionization method, Wen's model is mapped into a series of one-dimensional Ising interactions. Considering the boundary terms with this mapping then reveals how the Ising chains interact with one another. The relationships discussed in this paper allow us to consider these models from two different perspectives: From the perspective of condensed matter physics these mappings allow us to learn more about the relation between the ground state properties of the four different models, such as their entanglement or topological structure. On the other hand, we take the duality of these models as a starting point to address questions related to the universality of their ground states for quantum computation.Comment: 5 Figure