Related papers: Existence of the Schmidt decomposition for tripart…
We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, \Psi_0 or \Psi_1. We distribute the qubits to two parties, Alice and Bob. They each measure their qubit and then compare their…
We give necessary conditions for the mixing problem in bipartite case, which are independent of eigenvalues and based on algebraic-geometric invariants of the bipartite states. One implication of our results is that for some special…
This paper focuses on the geometric phase of entangled states of bi-partite systems under bi-local unitary evolution. We investigate the relation between the geometric phase of the system and those of the subsystems. It is shown that (1)…
Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any…
This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational…
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of…
Can vectors with low Schmidt rank form mutually unbiased bases? Can vectors with high Schmidt rank form positive under partial transpose states? In this work, we address these questions by presenting several new results related to Schmidt…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame…
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary…
Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In…
We examine two conditions that can be used to detect bipartite entanglement, and show that they can be used to provide lower bounds on the negativity of states. We begin with two-qubit states, and then show how what was done there can be…
We show theoretically that according to the disentanglement behavior under composite noise environment, the Hilbert space of a two-qubit system can be divided into two separate parts: a 3-dimensional subspace in which all states disentangle…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is…
Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in the light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal…
Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…