Algebraic and algorithmic frameworks for optimized quantum measurements

Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can be overcome by "wrapping" the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup-specific. We shall here develop a unified framework for designing optimized measurements. Our approach is two-fold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which---taken individually---have a low quantum efficiency can be be arranged into circuits where, collectively, the limitations of inefficiency are compensated for

Assessments of macroscopicity for quantum optical states

With the slow but constant progress in the coherent control of quantum systems, it is now possible to create large quantum superpositions. There has therefore been an increased interest in quantifying any claims of macroscopicity. We attempt here to motivate three criteria which we believe should enter in the assessment of macroscopic quantumness: The number of quantum fluctuation photons, the purity of the states, and the ease with which the branches making up the state can be distinguished

Realistic limits on the nonlocality of an N-partite single-photon superposition

A recent paper [L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, New Journal of Physics, 13, 053054 (2011)] revealed that a single quantum symmetrically delocalized over N modes, namely a W state, effectively allows for all-versus-nothing proofs of nonlocality in the limit of large N. Ideally, this finding opens up the possibility of using the robustness of the W states while realizing the nonlocal behavior previously thought to be exclusive to the more complex class of Greenberger-Horne-Zeilinger (GHZ) states. We show that in practice, however, the slightest decoherence or inefficiency of the Bell measurements on W states will degrade any violation margin gained by scaling to higher N. The non-statistical demonstration of nonlocality is thus proved to be impossible in any realistic experiment.Comment: 6 pages, 6 figure

Generation of picosecond pulsed coherent state superpositions

We present the generation of approximated coherent state superpositions - referred to as Schr\"odinger cat states - by the process of subtracting single photons from picosecond pulsed squeezed states of light at 830 nm. The squeezed vacuum states are produced by spontaneous parametric down-conversion (SPDC) in a periodically poled KTiOPO4 crystal while the single photons are probabilistically subtracted using a beamsplitter and a single photon detector. The resulting states are fully characterized with time-resolved homodyne quantum state tomography. Varying the pump power of the SPDC, we generated different states which exhibit non-Gaussian behavior.Comment: 17 pages, 8 figures, 3 table

Deterministic teleportation using single-photon entanglement as a resource

We outline a proof that teleportation with a single particle is in principle just as reliable as with two particles. We thereby hope to dispel the skepticism surrounding single-photon entanglement as a valid resource in quantum information. A deterministic Bell state analyzer is proposed which uses only classical resources, namely coherent states, a Kerr non-linearity, and a two-level atom.Comment: 6 pages, 4 figure

Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding

We present a scheme for the amplification of Schrodinger cats that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications.Comment: 11 pages, 15 figure

Experimental demonstration of a Hadamard gate for coherent state qubits

We discuss and experimentally demonstrate a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, non-classical resources and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment we simulate the fidelity for all coherent state qubits on the Bloch sphere