Mutual Unbiasedness in Coarse-grained Continuous Variables

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.Comment: 5 pages, 3 figures + Supplemental Material (1 page) v2: Introduction expanded, minor typos correcte

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyze the measurement of intensity correlations using multielement detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximizes the visibility of the two-photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying charge-coupled device camera, finding excellent agreement with the theoretical analysis

EPR-based ghost imaging using a single-photon-sensitive camera

Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work, we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein–Podolsky–Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing

Testing for entanglement with periodic coarse-graining

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate novel entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows for an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\sim60\%$ relative to $7344$ studied cases.Comment: V1: revtex4, 10 pages, 4 figures + supp. material (4 pages, 1 figure) V2: Substantial revisions implemented both in theory and experimental data analysi

Ruptures and repairs of group therapy alliance. an untold story in psychotherapy research

Although previous studies investigated the characteristics of therapeutic alliance in group treatments, there is still a dearth of research on group alliance ruptures and repairs. The model by Safran and Muran was originally developed to address therapeutic alliance in individual therapies, and the usefulness of this approach to group intervention needs to be demonstrated. Alliance ruptures are possible at member to therapist, member to member, member to group levels. Moreover, repairs of ruptures in group are quite complex, i.e., because other group members have to process the rupture even if not directly involved. The aim of the current study is to review the empirical research on group alliance, and to examine whether the rupture repair model can be a suitable framework for clinical understanding and research of the complexity of therapeutic alliance in group treatments. We provide clinical vignettes and commentary to illustrate theoretical and research aspects of therapeutic alliance rupture and repair in groups. Our colleague Jeremy Safran made a substantial contribution to research on therapeutic alliance, and the current paper illustrates the enduring legacy of this work and its potential application to the group therapy context

A tight Tsirelson inequality for infinitely many outcomes

We present a novel tight bound on the quantum violations of the CGLMP inequality in the case of infinitely many outcomes. Like in the case of Tsirelson's inequality the proof of our new inequality does not require any assumptions on the dimension of the Hilbert space or kinds of operators involved. However, it is seen that the maximal violation is obtained by the conjectured best measurements and a pure, but not maximally entangled, state. We give an approximate state which, in the limit where the number of outcomes tends to infinity, goes to the optimal state for this setting. This state might be potentially relevant for experimental verifications of Bell inequalities through multi-dimenisonal entangled photon pairs.Comment: 5 pages, 2 figures; improved presentation, change in title, as published