Related papers: Characterizing generalized axisymmetric quantum st…
The study of properties of randomly chosen quantum states has in recent years led to many insights into quantum entanglement. In this work, we study private quantum states from this point of view. Private quantum states are bipartite…
Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite…
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic…
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…
The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
We find that the m-separability and k-partite entanglement of a multipartite quantum system is correlated with quantum coherence of the same with respect to complete orthonormal bases, distinguishable under local operations and classical…
Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…
The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some…
The classification of multipartite entanglement is essential as it serves as a resource for various quantum information processing tasks. This study concerns a particular class of highly entangled multipartite states, the so-called…
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…
In this short note we show two completely opposite methods of constructing entangled states. Given a bipartite state $\gamma\in M_k\otimes M_k$, define $\gamma_S=(Id+F)\gamma (Id+F)$, $\gamma_A=(Id-F)\gamma(Id-F)$, where $F\in M_k\otimes…
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bi-partite quantum state-space. When the…
The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for…
We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure…
We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under…
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…