Related papers: Maximum entropy methods for quantum state compatib…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control has attracted much attention especially in…
In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…
Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In this work, an exact analytic solution to an optimum measurement problem involving an…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…
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…
In this PhD thesis, several aspects regarding maximal entanglement are analyzed. In the first chapter, Bell Inequalities are analyzed from an operational perspective as well as novel Bell inequalities are obtained together with their…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are…
Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…