Related papers: Optimal Perfect Distinguishability between Unitari…
We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or…
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate…
We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses…
Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch-Jozsa algorithm, Simon's algorithm, and Grover's algorithm can essentially be regarded…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
In this paper, we address the problem of discriminating two given quantum operations. Firstly, based on the Bloch representation of single qubit systems, we give the exact minimum error probability of discriminating two single qubit quantum…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
The notion of antidistinguishability captures the possibility of ruling out certain alternatives in a quantum experiment without identifying the actual outcome. Although extensively studied for quantum states, the antidistinguishability of…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…
The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always…
Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary…
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 prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
Recent developments have revealed deterministic and exact protocols for performing complex conjugation, inversion, and transposition of a general $d$-dimensional unknown unitary operation using a finite number of queries to a black-box…