Scalable Ellipsoidal Classification for Bipartite Quantum States

The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as separable, otherwise it will be taken as entangled. Our method is scalable and can be implemented straightforwardly in any desired dimension. Moreover, we show that it allows for detection of Bound Entangled StatesComment: 8 pages, 5 figures, 3 tables. Revised version, to appear in Physical Review

Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Quantum teleportation scheme by selecting one of multiple output ports

The scheme of quantum teleportation, where Bob has multiple (N) output ports and obtains the teleported state by simply selecting one of the N ports, is thoroughly studied. We consider both deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state, and (ii) the state is also optimized as well as Alice's measurement. We analytically determine the optimal protocols for all the four cases, and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\to\infty$. The entanglement properties of the teleportation scheme are also discussed.Comment: 14 pages, 4 figure

Big Data and the Internet of Things

Advances in sensing and computing capabilities are making it possible to embed increasing computing power in small devices. This has enabled the sensing devices not just to passively capture data at very high resolution but also to take sophisticated actions in response. Combined with advances in communication, this is resulting in an ecosystem of highly interconnected devices referred to as the Internet of Things - IoT. In conjunction, the advances in machine learning have allowed building models on this ever increasing amounts of data. Consequently, devices all the way from heavy assets such as aircraft engines to wearables such as health monitors can all now not only generate massive amounts of data but can draw back on aggregate analytics to "improve" their performance over time. Big data analytics has been identified as a key enabler for the IoT. In this chapter, we discuss various avenues of the IoT where big data analytics either is already making a significant impact or is on the cusp of doing so. We also discuss social implications and areas of concern.Comment: 33 pages. draft of upcoming book chapter in Japkowicz and Stefanowski (eds.) Big Data Analysis: New algorithms for a new society, Springer Series on Studies in Big Data, to appea

Cortical pain responses in human infants

Despite the recent increase in our understanding of the development of pain processing, it is still not known whether premature infants are capable of processing pain at a cortical level. In this study, changes in cerebral oxygenation over the somatosensory cortex were measured in response to noxious stimulation using real-time near-infrared spectroscopy in 18 infants aged between 25 and 45 weeks postmenstrual age. The noxious stimuli were heel lances performed for routine blood sampling; no blood tests were performed solely for the purpose of the study. Noxious stimulation produced a clear cortical response, measured as an increase in total hemoglobin concentration [HbT] in the contralateral somatosensory cortex, from 25 weeks (mean Delta[HbT] = 7.74 mu mol/L; SE, 1.10). Cortical responses were significantly greater in awake compared with sleeping infants, with a mean difference of 6.63 mu mol/L [95% confidence interval (CI) limits: 2.35, 10.91 mu mol/L; mean age, 35.2 weeks]. In awake infants, the response in the contralateral somatosensory cortex increased with age ( regression coefficient, 0.698 mu mol/L/week; 95% CI limits: 0.132, 1.265 mu mol/L/week) and the latency decreased with age (regression coefficient, -0.9861 mu mol/L/week; 95% CI limits: -1.5361, -0.4361 mu mol/L/week; age range, 25-38 weeks). The response was modality specific because no response was detected after non-noxious stimulation of the heel, even when accompanied by reflex withdrawal of the foot. We conclude that noxious information is transmitted to the preterm infant cortex from 25 weeks, highlighting the potential for both higher-level pain processing and pain-induced plasticity in the human brain from a very early age

Ultranarrow resonance peaks in the transmission and reflection spectra of a photonic crystal cavity with Raman gain

The Raman gain of a probe light in a three-state $\Lambda$-scheme placed into a defect of a one-dimensional photonic crystal is studied theoretically. We show that there exists a pump intensity range, where the transmission and reflection spectra of the probe field exhibit \textit{simultaneously} occurring narrow peaks (resonances) whose position is determined by the Raman resonance. Transmission and reflection coefficients can be larger than unity at pump intensities of order tens of $\mu$W/cm$^{2}$. When the pump intensity is outside this region, the peak in the transmission spectrum turns into a narrow dip. The nature of narrow resonances is attributed to a drastic dispersion of the nonlinear refractive index in the vicinity of the Raman transition, which leads to a significant reduction of the group velocity of the probe wave.Comment: 9 pages, 3 figure

How to identify the youngest protostars

We study the transition from a prestellar core to a Class 0 protostar, using SPH to simulate the dynamical evolution, and a Monte Carlo radiative transfer code to generate the SED and isophotal maps. For a prestellar core illuminated by the standard interstellar radiation field, the luminosity is low and the SED peaks at ~190 micron. Once a protostar has formed, the luminosity rises (due to a growing contribution from accretion onto the protostar) and the peak of the SED shifts to shorter wavelengths (~80-100 micron). However, by the end of the Class 0 phase, the accretion rate is falling, the luminosity has decreased, and the peak of the SED shifts back towards longer wavelengths (90-150 micron). In our simulations, the density of material around the protostar remains sufficiently high well into the Class 0 phase that the protostar only becomes visible in the NIR if it is displaced from the centre dynamically. Raw submm/mm maps of Class 0 protostars tend to be much more centrally condensed than those of prestellar cores. However, when convolved with a typical telescope beam, the difference in central concentration is less marked, although the Class 0 protostars appear more circular. Our results suggest that, if a core is deemed to be prestellar on the basis of having no associated IRAS source, no cm radio emission, and no outflow, but it has a circular appearance and an SED which peaks at wavelengths below ~170 micron, it may well contain a very young Class 0 protostar.Comment: Accepted by A&A (avaliable with high-res images at http://carina.astro.cf.ac.uk/pub/Dimitrios.Stamatellos/publications

Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product

Minimum error state discrimination between two mixed states \rho and \sigma can be aided by the receipt of "classical side information" specifying which states from some convex decompositions of \rho and \sigma apply in each run. We quantify this phenomena by the average trace distance, and give lower and upper bounds on this quantity as functions of \rho and \sigma. The lower bound is simply the trace distance between \rho and \sigma, trivially seen to be tight. The upper bound is \sqrt{1 - tr(\rho\sigma)}, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of "unbiased decompositions", which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of non-classicality known as preparation contextuality.Comment: 3 pages, 1 figure. v2: Less typos in text and less punctuation in titl

Robust Quantum Error Correction via Convex Optimization

We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity. We illustrate our theory numerically for optimized 5-qubit codes, using the standard [5,1,3] code as a benchmark. Our optimized encoding and recovery yields fidelities that are uniformly higher by 1-2 orders of magnitude against random unitary weight-2 errors compared to the [5,1,3] code with standard recovery. We observe similar improvement for a 4-qubit decoherence-free subspace code.Comment: 4 pages, including 3 figures. v2: new example