Optimal pulse spacing for dynamical decoupling in the presence of a purely-dephasing spin-bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system-qubits are 13C nuclear spins and the environment consists of a 1H nuclear spin-bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs superior to any non-equidistant DD sequence in the presence of this kind of environmental noise.Comment: To be published in Phys. Rev. A. 15 pages, 16 figures. Presentation of the work was improved. One Figure and some Refs. were adde

Analysis of models of coherence of spectral non-stationality of random signals

В статті проведено аналіз ймовірнісних властивостей частотно-часової моделі когерентності, аналіз впливу локальних властивостей базисної функції вейлет-перетворення на параметри моделі автокогерентності, дисперсійний аналіз частотної та часової моделей когерентності, розширено простір параметрів настаціонарності (для вирішення задачі першого етапу синтезу інформаційно-вимірювальної системи контролю та діагностування динамічних об'єктів – створення багатовимірної системи інформативних параметрів контролю динамічних властивостей об'єкту в умовах апріорної невизначеності математичних моделей нестаціонарності). В статті визначені умови вибору числа масштабів та зсувів при оцінці коефіцієнтів автокогерентності для задачі контролю порушень стаціонарності вимірювального сигналу, отримані умови калібрування показника автокогерентності, що відповідають відсутності порушення стаціонарності, розроблено імовірнісна модель показника автокогерентності, що враховує мінімальне значення масштабу спектрального вейвлет-перетворення, показана можливість дисперсійного розкладання базового показника автокогерентності на парні незалежні складові які дозволяють отримати незалежну інформацію про порушення стаціонарності з урахуванням функціональних та випадкових змін спектру. За результатами дослідження отримала розвиток теорія автокогерентності спектрально нестаціонарних вимірювальних сигналів. Визначені умови вибору числа масштабів та зсувів при оцінці коефіцієнтів автокогерентності для задачі контролю порушень стаціонарності вимірювального сигналу. Дослідження виконані для вирішення науково-практичної проблеми недосконалості та обмеженості теоретичного обґрунтування при створенні комп'ютеризованих інформаційно-вимірювальних пристроїв контролю та діагностування динамічних об'єктів, локально і глобально нестаціонарних за своїми спектральними властивостями.The article analyzes the probabilistic properties of the frequency-time model of coherence, analyzes the influence of local properties of the basis function of the wavelet transform on the parameters of the autocoherence model, the dispersion analysis of the frequency and time models of coherence, expanded the space of parameters of the stationary (for solving the problem of the first stage of the synthesis of information-measuring control system and the diagnostics of dynamic objects - the creation of a multidimensional system of informative control parameters of dynamic inherent Tay subject under a priori uncertainty of mathematical models of non-stationary). The conditions of the choice of the number of scales and landslides in the estimation of the coefficients of auto-coherence for the task of monitoring the disturbances of the measuringsignal stationary are obtained, the conditions of calibration of the auto-coherence index corresponding to the absence ofstationary violation are determined, the probabilistic model of the auto-coherence index taking into account the minimum value of the scale of the spectral wavelet transform is shown the possibility of dispersion expansion of the basic index of auto-coherence on the paired independent components of which allow to obtain independent information on stationary violation, taking into account functional and random changes of the spectrum. According to the results of the study, the theory of autocorrelation of spectral non-stationary measurement signals was developed. The conditions of the choice of the number of scales and landslides are determined in the estimation of the coefficients of auto-coherence for the task of monitoring the disturbances of the stationary signal of the measuring signal. The research is carried out to solve the scientific and practical problem of imperfection and limitationsof theoretical substantiation in the creation of computerized information measuring devices for monitoring and diagnosing dynamic objects locally and globally unsteady in their spectral properties

Passive Scene Reconstruction in Non-line-of-sight Scenarios

Locating and identifying hidden objects can prove critical in applications ranging from military reconnaissance to emergency rescue. Although non-line-of-sight (NLOS) reconstruction and imaging have received much attention recently, state-of-the-art methods often use coherent sources (lasers) or require control of the scene. This dissertation focuses on passive NLOS scene reconstruction using the light reflected off a diffusive wall. No control over the light illuminating the scene is assumed, and the method is compatible with the partially coherent fields ubiquitous in both indoor and outdoor environments. In order to counteract the detrimental effects of the wall, rather than measuring the 2-dimensional intensity of the reflected light, we exploit the full 4-dimensional spatial coherence function to reconstruct the scene. As a step towards the NLOS problem, we first consider the line-of-sight (LOS) problem. Numerical simulations using Fresnel propagation operators show that our forward model has good agreement with experimental results. We show that numerically back-propagating the measured coherence function enables a visual estimation of the objects\u27 sizes and locations. To facilitate efficient, systematic and explicit detection of object parameters in the inverse problem, we propose a closed-form approximation of the propagated coherence function. Using this analytic solution we formulate a minimum residue optimization problem which is solved using a gradient descent algorithm. Then, for the NLOS problem, we derive an analytic model based on experimentally-verified scattering models. This model is used to study the information retained in the coherence function after the field interacts with the wall, and this insight is used to classify and estimate simple objects. Finally, we consider imaging in more complicated settings with larger objects. We formulate a multi-criteria convex optimization problem, which fuses the reflected field\u27s intensity and spatial coherence information at different scales, along with an algorithm to efficiently solve the proposed problem

Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach

A key challenge of massive MTC (mMTC), is the joint detection of device activity and decoding of data. The sparse characteristics of mMTC makes compressed sensing (CS) approaches a promising solution to the device detection problem. However, utilizing CS-based approaches for device detection along with channel estimation, and using the acquired estimates for coherent data transmission is suboptimal, especially when the goal is to convey only a few bits of data. First, we focus on the coherent transmission and demonstrate that it is possible to obtain more accurate channel state information by combining conventional estimators with CS-based techniques. Moreover, we illustrate that even simple power control techniques can enhance the device detection performance in mMTC setups. Second, we devise a new non-coherent transmission scheme for mMTC and specifically for grant-free random access. We design an algorithm that jointly detects device activity along with embedded information bits. The approach leverages elements from the approximate message passing (AMP) algorithm, and exploits the structured sparsity introduced by the non-coherent transmission scheme. Our analysis reveals that the proposed approach has superior performance compared to application of the original AMP approach.Comment: Submitted to IEEE Transactions on Communication

Spectral Efficiency of Mixed-ADC Massive MIMO

We study the spectral efficiency (SE) of a mixed-ADC massive MIMO system in which K single-antenna users communicate with a base station (BS) equipped with M antennas connected to N high-resolution ADCs and M-N one-bit ADCs. This architecture has been proposed as an approach for realizing massive MIMO systems with reasonable power consumption. First, we investigate the effectiveness of mixed-ADC architectures in overcoming the channel estimation error caused by coarse quantization. For the channel estimation phase, we study to what extent one can combat the SE loss by exploiting just N << M pairs of high-resolution ADCs. We extend the round-robin training scheme for mixed-ADC systems to include both high-resolution and one-bit quantized observations. Then, we analyze the impact of the resulting channel estimation error in the data detection phase. We consider random high-resolution ADC assignment and also analyze a simple antenna selection scheme to increase the SE. Analytical expressions are derived for the SE for maximum ratio combining (MRC) and numerical results are presented for zero-forcing (ZF) detection. Performance comparisons are made against systems with uniform ADC resolution and against mixed-ADC systems without round-robin training to illustrate under what conditions each approach provides the greatest benefit.Comment: To appear in IEEE Transactions on Signal Processin

Downlink Training in Cell-Free Massive MIMO: A Blessing in Disguise

Cell-free Massive MIMO (multiple-input multiple-output) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works demonstrated that, unlike co-located Massive MIMO, the \textit{channel hardening} is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the previously proposed analysis to non-orthogonal uplink and downlink pilots. Assuming single-antenna APs, conjugate beamforming and independent Rayleigh fading channel, we derive a closed-form expression for the per-user achievable downlink rate that addresses channel estimation errors and pilot contamination both at the AP and UE side. The performance evaluation includes max-min fairness power control, greedy pilot assignment methods, and a comparison between achievable rates obtained from different capacity-bounding techniques. Numerical results show that downlink beamforming training, although increases pilot overhead and introduces additional pilot contamination, improves significantly the achievable downlink rate. Even for large number of APs, it is not fully efficient for the UE relying on the statistical channel state information for data decoding.Comment: Published in IEEE Transactions on Wireless Communications on August 14, 2019. {\copyright} 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other use