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Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local realism and determine a bound on the probability, according to local realism, of obtaining a violation at least that observed. In general, it is difficult to obtain sufficiently robust and small bounds. Here we describe an efficient protocol for computing such bounds from any set of Bell inequalities for any number of parties, measurement settings, or outcomes. The protocol can be applied to tests of other properties (such as entanglement or dimensionality) that are witnessed by linear inequalities., Comment: 9 pages, 3 figures

When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically prepared systems. The optimization is usually performed with iterative algorithms. This paper provides a gradient-based upper bound on the ratio of the true maximum likelihood and the likelihood of the state of the current iteration, regardless of the particular algorithm used. This bound is useful for formulating stopping rules for halting iterations of maximization algorithms. We discuss such stopping rules in the context of determining confidence regions from log-likelihood differences when the differences are approximately chi-squared distributed., Comment: 9 pages, single column, 1 figure. Updated to accepted manuscript version. Now includes section headings and other small editorial changes

Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p-value. We propose a prediction-based-ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p-values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, arXiv:quant-ph/0110137]. We find that the p-values of the former can be too small and are therefore not statistically valid, while those derived from the latter are sub-optimal. PBR p-values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details., Comment: 11 pages, 4 figures; Software implementation of the PBR analysis protocol and its user guide attached as ancillary files; minor changes (add the software disclaimer, etc.)

We characterize a periodically poled KTP crystal that produces an entangled, two-mode, squeezed state with orthogonal polarizations, nearly identical, factorizable frequency modes, and few photons in unwanted frequency modes. We focus the pump beam to create a nearly circular joint spectral probability distribution between the two modes. After disentangling the two modes, we observe Hong-Ou-Mandel interference with a raw (background corrected) visibility of 86 % (95 %) when an 8.6 nm bandwidth spectral filter is applied. We measure second order photon correlations of the entangled and disentangled squeezed states with both superconducting nanowire single-photon detectors and photon-number-resolving transition-edge sensors. Both methods agree and verify that the detected modes contain the desired photon number distributions.

We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a pre-amplifier to improve the quantum efficiency of the field quadrature measurement (QM) from 2% to 36 +/- 4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 69 +/- 8% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics., Comment: 8 pages, 5 figures, published version to contain higher resolution figures

Both discrete and continuous systems can be used to encode quantum information. Most quantum computation schemes propose encoding qubits in two-level systems, such as a two-level atom or an electron spin. Others exploit the use of an infinite-dimensional system, such as a harmonic oscillator. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schr\"odinger cat states"), squeezing, linear optical devices, and homodyne detection., Comment: 4 pages, 3 figures. Submitted to Optics Letters

We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 -0.24/+0.06 and a fidelity of 0.59 -0.14/+0.04 with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs., Comment: Main manuscript and supplementary material

Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiency required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least 89.71%, or photon detectors with efficiencies of at least 91.11%. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above 2/3., Comment: 18 pages, 3 figures, minor changes (add more references, replace the old plots, etc.).

We discuss several methods to produce superpositions of optical coherent states (also known as "cat states"). Cat states have remarkable properties that could allow them to be powerful tools for quantum information processing and metrology. A number of proposals for how one can produce cat states have appeared in the literature in recent years. We describe these proposals and present new simulation and analysis of them incorporating practical issues such as photon loss, detector inefficiency, and limited strength of nonlinear interactions. We also examine how each would perform in a realistic experiment., Comment: 25 pages, 27 figures, revtex. Version 2 includes expanded discussion of some earlier methods and more references. Version 3 includes even more references and a more conclusive conclusion. Version 3 is the published version

We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error-correcting code on his or her qubits. The parties exchange their measurement results, detect or correct errors, and decode the desired purified state. We give sufficient conditions on the stabilizer codes that may be used in this procedure and find that Steane's seven-qubit code is the smallest error-correcting code sufficient to purify any stabilizer state. An error-detecting code that encodes two qubits in six can also be used to purify any stabilizer state. We further specify which classes of stabilizer codes can purify which classes of stabilizer states., Comment: 11 pages, 0 figures, comments welcome, submitting to Physical Review A