Related papers: SIC-POVMs and Compatibility among Quantum States
We study the geometric measure of entanglement (GM) of pure symmetric states related to rank-one positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
Sufficient and necessary conditions are presented for the existence of $(N,M)$-positive operator valued measures ($(N,M)$-POVMs) valid for arbitrary-dimensional quantum systems. A sufficient condition for the existence of $(N,M)$-POVMs is…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The discrimination of quantum states is a central problem in quantum information science and technology. Meanwhile, partial post-selection has emerged as a valuable tool for quantum state engineering. In this work, we bring these two areas…
We introduce and explore two questions concerning spectra of operators that are of interest in the theory of entanglement in symmetric (i.e., bosonic) quantum systems. First, we investigate the inverse eigenvalue problem for symmetric…
Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its…
Two-mode cavities can be prepared in quantum states which represent symmetric multi-qubit states. However, the qubits are impossible to address individually and as such cannot be independently measured or otherwise manipulated. We propose…
We analyze bipartite quantum states that admit a symmetric extension. Any such state can be decomposed into a convex combination of states that allow a _pure_ symmetric extension. A necessary condition for a state to admit a pure symmetric…
In relation of observable and quantum state, the entity $I_C$ from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this article its application to quantum correlations in bipartite states is studied.…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
The state that an observer attributes to a quantum system depends on the information available to that observer. If two or more observers have different information about a single system, they will in general assign different states. Is…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC…
Informationally complete measurements are a dramatic discovery of quantum information science, and the symmetric IC measurements, known as SICs, are in many ways optimal among them. Close study of three of the "sporadic SICs" reveals an…
Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
Coherence is a cornerstone of quantum theory and a prerequisite for the advantage of quantum technologies. In recent work, the notion of coherence with respect to a general quantum measurement (POVM) was introduced and embedded into a…