Related papers: Multilinear quantum Lie operations
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including…
We study the behaviour of quantum field theories defined on a surface $S$ as it tends to a null surface $S_n$. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of…
Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible…
The prepare-and-measure scenario offers the possibility to infer the dimension of an unknown physical system in a device-independent way, i.e. using only raw measurement data with apparatuses regarded as black boxes. We provide here a…
Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A \textbf{61}, 042311 (2000)] is revisited based on a…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of…
Quantum coherence is a basic feature of quantum physics. Combined with tensor product structure of state space, it gives rise to the novel concepts such as entanglement and quantum correlations, which play a crucial role in quantum…
This manuscript was published as a JINR Preprint E17-10550 in 1977. In view of the recent interest in various new kinds of statistics it seems the results it contains may be still of some interest. It is shown that the second quantization…
Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
Lie quasi-states on a real Lie algebra are functionals which are linear on any abelian subalgebra. We show that on the symplectic Lie algebra of rank at least 3 there is only one continuous non-linear Lie quasi-state (up to a scalar factor,…
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all…
We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a…
Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental…
In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…
This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and…