Related papers: Optimal Error Exponents for Composite Sequential Q…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
Deterministic discrimination of nonorthogonal states is forbidden by quantum measurement theory. However, if we do not want to succeed all the time, i.e. allow for inconclusive outcomes to occur, then unambiguous discrimination becomes…
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 novel group testing method, termed semi-quantitative group testing, motivated by a class of problems arising in genome screening experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary pooling scheme that…
We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a…
Quantum computing promises to solve problems previously deemed infeasible. However, high error rates necessitate quantum error correction for practical applications. Seminal experiments with zoned neutral atom architectures have shown…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
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 develop error-tolerant quantum state discrimination(QSD) strategies that maintain reliable performance under moderate noise. Two complementary approaches are proposed: CrossQSD, which generalizes unambiguous discrimination with tunable…
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the…
We derive the optimal exponent of the error probability of the quantum fixed-length pure state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81, 1714…
The optimal error exponents of binary composite i.i.d. state discrimination are trivially bounded by the worst-case pairwise exponents of discriminating individual elements of the sets representing the two hypotheses, and in the…
We revisit $M$-ary classification of Gutman (TIT 1989), where one is tasked to determine whether a testing sequence is generated with the same distribution as one of the $M$ training sequences or not. Our main result is a two-phase test,…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We address the problem of optimal estimation of the relative phase for two-dimensional quantum systems in mixed states. In particular, we derive the optimal measurement procedures for an arbitrary number of qubits prepared in the same mixed…
The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
We propose a novel finite-sample procedure for testing composite null hypotheses. Traditional likelihood ratio tests based on asymptotic $\chi^2$ approximations often exhibit substantial bias in small samples. Our procedure rejects the…