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One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a…
We study the relative error of the state-dependent N=>L cloning. A copying transformation and dimension of state space are not specified. Only the unitarity of quantum mechanical transformations is used. The proposed approach is based on…
The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states $\sigma_{AB}=…
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are…
We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
Quantum information is nonlocal in the sense that local measurements on a composite quantum system, prepared in one of many mutually orthogonal states, may not reveal in which state the system was prepared. It is shown that in the many copy…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to…
Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…
Quantum devices for generating entangled states have been extensively studied and widely used. As so, it becomes necessary to verify that these devices truly work reliably and efficiently as they are specified. Here, we experimentally…
The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…