Related papers: On Error Exponents in Quantum Hypothesis Testing
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
The paper estimates the Chernoff rate for the efficiency of quantum hypothesis testing. For both joint and separable measurements, approximate bounds for the rate are given if both states are mixed and exact expressions are derived if at…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…