Teleportation is necessary for faithful quantum state transfer through noisy channels of maximal rank

Quantum teleportation enables deterministic and faithful transmission of quantum states, provided a maximally entangled state is pre-shared between sender and receiver, and a one-way classical channel is available. Here, we prove that these resources are not only sufficient, but also necessary, for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the cannel is admitted. In other words, for this family of channels, there are no other protocols, based on different (and possibly cheaper) sets of resources, capable of replacing quantum teleportation.Comment: 4 pages, comments are welcom

Distillation of mixed-state continuous-variable entanglement by photon subtraction

We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beamsplitters and coherent photon-detection techniques, including conventional on-off detectors and photon number resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beamsplitter is derived, representing the minimal value that still allows to enhance the entanglement.Comment: 13 pages, 8 figure

Building Gaussian Cluster States by Linear Optics

The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. We show that for any Gaussian cluster state, the canonical generation scheme in terms of QND-type interactions, can be entirely replaced by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful and we propose a systematic way to create cheaper states. As an application, we consider Gaussian cluster computation in multiple-rail encoding. This encoding may reduce errors due to finite squeezing, even when the extra rails are achieved through off-line squeezing and linear optics.Comment: 5 Pages, 3 figure

Universal Quantum Computation with Continuous-Variable Cluster States

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.Comment: 4 pages, no figure

Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state

We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In the entanglement swapping process, a four--partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot noise, which is due to the potential four--party entanglement.Comment: 9 pages, 10 figures, update of references 9 and 10; minor inconsistency in notation removed; format for units in the figures change

Quantum Computing with Continuous-Variable Clusters

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.Comment: 17 pages, 5 figure

Entanglement properties of optical coherent states under amplitude damping

Through concurrence, we characterize the entanglement properties of optical coherent-state qubits subject to an amplitude damping channel. We investigate the distillation capabilities of known error correcting codes and obtain upper bounds on the entanglement depending on the non-orthogonality of the coherent states and the channel damping parameter. This work provides a first, full quantitative analysis of these photon-loss codes which are naturally reminiscent of the standard qubit codes against Pauli errors.Comment: 7 pages, 6 figures. Revised version with small corrections; main results remain unaltere

Greenberger-Horne-Zeilinger paradox for continuous variables

We show how to construct states for which a Greenberger-Horne-Zeilinger type paradox occurs if each party measures either the position or momentum of his particle. The paradox can be ascribed to the anticommutation of certain translation operators in phase space. We then rephrase the paradox in terms of modular and binary variables. The origin of the paradox is then due to the fact that the associativity of addition of modular variables is true only for c-numbers but does not hold for operators.Comment: 4 pages, no figure