Related papers: A List of Complexity Bounds for Property Testing b…
We study the query complexity of testing for properties defined by read once formulas, as instances of {\em massively parametrized properties}, and prove several testability and non-testability results. First we prove the testability of any…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
Quantifying the complexity of quantum states that possess intrinsic structure, such as symmetry or encoding, in a fair manner constitutes a core challenge in the benchmarking of quantum technologies. This paper introduces the…
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…
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to…
Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs…
One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight…
Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…
Although a concept class may be learnt more efficiently using quantum samples as compared with classical samples in certain scenarios, Arunachalam and de Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more efficient…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which…
I offer a case that quantum query complexity still has loads of enticing and fundamental open problems -- from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial…
We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable…
In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…
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…
Although classical computing has excelled in a wide range of applications, there remain problems that push the limits of its capabilities, especially in fields like cryptography, optimization, and materials science. Quantum computing…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…