Related papers: Beyond Hoeffding and Chernoff: Trading conclusiven…
Quantum state discrimination involves identifying a given state out of a set of possible states. When the states are mutually orthogonal, perfect state discrimination is always possible using a global measurement. In the case of…
In this paper we extend both standard fault tolerance theory and Kitaev's model for quantum computation, combining them so as to yield quantitative results that reveal the interplay between the two. Our analysis establishes a methodology…
Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big)…
We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…
We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…
Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal. In an adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
Free will (or randomness) has been studied to achieve loophole-free Bell's inequality test and to provide device-independent quantum key distribution security proofs. The required randomness such that a local hidden variable model (LHVM)…
This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
Unpredictability, or randomness, of the outcomes of measurements made on an entangled state can be certified provided that the statistics violate a Bell inequality. In the standard Bell scenario where each party performs a single…
The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We…
Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose…
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication…
We examine a new class of channel coding strategies, and hypothesis tests referred to as almost-fixed-length strategies that have little flexibility in the stopping time over fixed-length strategies. The stopping time of these strategies is…
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state $\rho$ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all…
The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore…