Related papers: LU transformation invariant operators and LU trans…
The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for both theoretical and practical reasons. As LOCC has a…
Multi-photon states are widely applied in quantum information technology. By the methods presented in this paper, the structure of a multi-photon state in the form of multiple single photon qubit product can be mapped to a single photon…
We consider the transformation of multi-partite states in the single copy setting under positive-partial-transpose-preserving operations (PPT-operations) and obtain both qualitative and quantitative results. Firstly, for some pure state…
We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…
Darboux transformations are viewed as morphisms in a Darboux category. Darboux transformations of type I which we defined previously, make an important subgroupoid consists of Darboux transformations of type I. We describe the orbits of…
The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT…
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
The concept of directionally unbiased optical multiports is introduced, in which photons may reflect back out the input direction. A linear-optical implementation is described, and the simplest three-port version studied. Symmetry arguments…
Consider a $k$-valued network. Two kinds of (control) invariant subspaces, called state and dual invariant subspaces, are proposed, which are subspaces of state space and dual space respectively. Algorithms are presented to verify whether a…
We propose a scheme to realize quantum logic and entanglement for qutrit systems via state-dependent forces on trapped ions. By exploiting the laser-ion coupling in the presence of Coulomb interactions, the set of quantum gate operations…
For pure symmetric 3-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal C$, the 3-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for…
Multipartite quantum correlations, in spite of years of intensive research, still leave many questions unanswered. While bipartite entanglement is relatively well understood for Gaussian states, the complexity of mere qualitative…
In the paper we introduce a general approach how for a given virtual biquandle multi-switch $(S,V)$ on an algebraic system $X$ (from some category) and a given virtual link $L$ construct an algebraic system $X_{S,V}(L)$ (from the same…
Effect of Lorentz transformation on some properties of multi-qubit systems is investigated. It is shown that, properties like, the fidelity and entanglement decay as the Wigner's angles increase, but can be improved, if all the transformed…
After quantum computers come out, governments and rich companies will have the abilities to buy these useful quantum computers, meanwhile they are familiar with these technologies proficiently. If a client wants to perform quantum computing…
We construct the protocols to achieve probabilistic and deterministic entanglement transformations for bipartite pure states by means of local operations and classical communication. A new condition on pure contraction transformations is…
We show that a single polynomial entanglement measure is enough to verify equivalence between generic $n$-qubit states under Stochastic Local Operations with Classical Communication (SLOCC). SLOCC operations may be represented geometrically…
The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic…
The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter…