Related papers: Symmetric quantum joint measurements on multiple q…
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…
Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moir\'e materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor,…
In order to study N-locality without inputs in long lines and in configurations with loops, e.g. the triangle, we introduce a natural joint measurement on two qubits different from the usual Bell state measurement. The resulting quantum…
We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2)…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
Symmetry restrictions limit the types of tasks that can be achieved with a given set of quantum states. Therefore, any breaking of these symmetries could potentially be exploited as a resource for quantum communication. Here we demonstrate…
Some quantum information processing protocols necessitate quantum operations that are invariant under complex conjugation. In this study, we analyze the non-local resources necessary for implementing conjugation-symmetric measurements on…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and…
We study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure…
The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which…
Generalised quantum measurements go beyond the textbook concept of a projection onto an orthonormal basis in Hilbert space. They are not only of fundamental relevance but have also an important role in quantum information tasks. However, it…
We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the…
We present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit…
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to…