Related papers: Entanglement in SO(3)-invariant bipartite quantum …
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can…
There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…
Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local…
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that this is true in most cases if the number of product vectors is…
In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states,…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett. \textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say…
We present an unambiguous characterization of the rotation group SO(3) biconnectedness topology using two-qubit maximally entangled states. We show how to generate cyclic evolutions of these states, which are in one-to-one correspondence to…
We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a…
We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states.
We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as…
Symmetry plays an important role in the field of quantum mechanics. In this paper, we consider a subclass of symmetric quantum states in the multipartite system $N^{\otimes d}$, namely, the completely symmetric states, which are invariant…
The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally…
Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…