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In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
Privacy-preserving average consensus aims to guarantee the privacy of initial states and asymptotic consensus on the exact average of the initial value. In existing work, it is achieved by adding and subtracting variance decaying and…
One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus,…
We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\cal{H}$, of any number of parties. Restricting consideration to measurements that act only on…
In the topic of perfect local distinguishability of orthogonal multipartite quantum states, most results obtained so far pertain to bipartite systems whose subsystems are of specific dimensions. In contrast very few results for bipartite…
We consider multi-party quantum sequence discrimination under local operations and classical communication(LOCC), and provide conditions under which the optimal LOCC discrimination of a multi-party quantum sequence ensemble can be…
Entangled quantum states are regarded as a key resource in quantum key distribution (QKD) protocols. However, quantum correlations, other than entanglement can also play a significant role in the QKD protocols. In this work, we will focus…
We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…
Quantum discord represents a correlation beyond classicality that could be useful for many quantum information tasks, and therefore is viewed as a valuable quantum resource. Theoretically, whether a bipartite quantum state has a non-zero…
A new measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a…
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the…
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…
A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(\xi_1, \xi_2,\xi_3)$…
Modern machine learning embeddings provide powerful compression of high-dimensional data, yet they typically destroy the geometric structure required for classical likelihood-based statistical inference. This paper develops a rigorous…
Quantum information masking is a protocol that hides the original quantum information from subsystems and spreads it over quantum correlation, which is available to multipartite except bipartite systems. In this work, we explicitly study…
The class of quantum operations known as Local Operations and Classical Communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has…