Related papers: Toward Instance-Optimal State Certification With I…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…
We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…
Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior…
We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…
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 investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
In this letter we consider the problem of certification of quantum measurements with an arbitrary number of outcomes. We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common…
There has been significant interest in understanding how practical constraints on contemporary quantum devices impact the complexity of quantum learning. For the classic question of tomography, recent work tightly characterized the copy…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
A central task in quantum information science is state certification: testing whether an unknown state is $\epsilon_1$-close to a fixed target state, or $\epsilon_2$-far. Recent work has shown that surprisingly simple measurement…
In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is…
We propose new optimality criterion for the estimation of state-dependent cloning. We call this measure the relative error because the one compares the errors in the copies with contiguous size taking into account the similarity of states…
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in…
We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state $\rho$ in order to learn a classical description which suffices to…