Related papers: Strict Hierarchy for Quantum Channel Certification…
Given a quantum channel and a state which satisfy a fixed point equation approximately (say, up to an error $\varepsilon$), can one find a new channel and a state, which are respectively close to the original ones, such that they satisfy an…
We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private…
We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination…
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 consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in…
We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel…
Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity…
Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in…
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
Amplitude damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the…
Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries…
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…
We analyze a discrimination problem of a single-qubit unitary gate with two candidates, where the candidates are not provided with their classical description, but their quantum sample is. More precisely, there are three unitary quantum…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
We formalize and study the Hamiltonian certification problem. Given access to $e^{-\mathrm{i} Ht}$ for an unknown Hamiltonian $H$, the goal of the problem is to determine whether $H$ is $\varepsilon_1$-close to or $\varepsilon_2$-far from a…