相关论文: Characterization of entanglement transformation vi…
Unitary metaplectic representations of the group $SL_2(\mathbb{Z}_{2^n})$ are necessary to describe the evolution of $2^n$-dimensional quantum systems, such as systems involving $n$ qubits. It is shown that in order for the metaplectic…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
The structure of the state spaces of bipartite (N tensor N) quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of…
We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
It is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the orthochronous proper Lorentz group $SO(1,3)\uparrow$. This…
By virtue of the integration method within P-ordered product of operators and the property of entangled state representation, we reveal new physical interpretation of the generalized two-mode squeezing operator (GTSO), and find it be…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…
We construct quantum evolution operators on the space of states, that realize the metaplectic representation of the modular group SL(2,Z_2^n). This representation acts in a natural way on the coordinates of the non-commutative 2-torus and…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
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…
We prove that convex-cocompact representations of finitely generated groups in the group of isometries of the infinite-dimensional hyperbolic space form an open set in the space of representations, allowing us to deform these…
The Lorentz transformation group $SO(m,n)$ is a group of Lorentz transformations of order $(m,n)$, that is, a group of special linear transformations in a pseudo-Euclidean space of signature $(m,n)$ that leave the pseudo-Euclidean inner…
It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…
All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…