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Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…
Recent proposals of measuring bipartite Renyi entropy experimentally involve techniques that hold exactly for non-interacting quantum particles. Here we consider the difference between such measurements and the actual Renyi entropy for…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
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…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary {\it Swap} operator acting on two copies of the system. An…
We analyse the reconstruction of an unknown pure qubit state. We derive the optimal guess that can be inferred from any set of measurements on N identical copies of the system with the fidelity as a figure of merit. We study in detail the…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum…
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
We present a scheme for measuring R\'enyi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random…
We introduce a method that allows one to infer many properties of a quantum state -- including nonlinear functions such as R\'enyi entropies -- using only global control over the constituent degrees of freedom. In this protocol, the state…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…