Related papers: Quantum Sequential Hypothesis Testing
We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular,…
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…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.
We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states, and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Quantum phase classification is a fundamental problem in quantum many-body physics, traditionally approached using order parameters or quantum machine learning techniques such as quantum convolutional neural networks (QCNNs). However, these…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
Quantum programs often produce probability distributions rather than deterministic outputs, making verification inherently statistical and increasingly costly on real hardware. In practice, developers still frequently rely on testing with…
Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. A set of quantum states is said to admit state exclusion if there exists a measurement whose…
Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…