Related papers: Approximate simulation of quantum channels
We investigate the space complexity of two graph streaming problems: Max-Cut and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and Krachun [STOC `19] resolved the classical complexity of the \emph{classical} problem,…
The common approach of designing a communication device is to maximize a well-defined objective function, e.g., the channel capacity and the cut-off rate. We propose easy-to-implement solutions for Gaussian channels that approximate the…
The essence of quantum error-correction is to use redundant Hilbert space to identify and correct errors, and the channel fidelity of the quantum channel does not affect which errors can be identified and corrected. Based on this, it is…
This paper is concerned with an elliptic optimal control problem with total variation (TV) restriction on the control in the constraints. We introduce a regularized optimal control problem by applying a quadratic regularization of the dual…
Broadcasting quantum and classical information is a basic task in quantum information processing, and is also a useful model in the study of quantum correlations including quantum discord. We establish a full operational characterization of…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with…
In this work, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength $n$ when the transmission rates approach the channel capacity at a rate slower than $1/\sqrt{n}$, a research topic known…
We consider the problem of bounded-error quantum state identification: given either state \alpha_0 or state \alpha_1, we are required to output `0', `1' or `?' ("don't know"), such that conditioned on outputting `0' or `1', our guess is…
The optimal coordination rates are determined in three primary settings of multi-user quantum networks, thus characterizing the minimal resources required in order to simulate a joint quantum state among multiple parties. We study the…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that…
We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the…
The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state,…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be…
A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the…
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…