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This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li \cite{CGHL21} showed the existence of asymptotically…
The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
In order to realize fault-tolerant quantum computation, tight evaluation of error threshold under practical noise models is essential. While non-Clifford noise is ubiquitous in experiments, the error threshold under non-Clifford noise…
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…
This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements. We propose to estimate the signals…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We…
We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the…
The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian…
Observation of even a single massive cluster, especially at high redshift, can falsify the standard cosmological framework consisting of a cosmological constant and cold dark matter (LCDM) with Gaussian initial conditions by exposing an…
We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations.…