Related papers: A Converse Bound via the Nussbaum-Szko{\l}a Mappin…
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we…
The uncertainty of measurement on a quantum system can be reduced in presence of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
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…
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 quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
Currently available quantum computers, so called Noisy Intermediate-Scale Quantum (NISQ) devices, are characterized by relatively low number of qubits and moderate gate fidelities. In such scenario, the implementation of quantum error…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum…
This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…
We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than…