Related papers: No-Cloning Theorem on Quantum Logics

We investigate the connection between quantum no-cloning theorem and Bell's theorem. Designing some Bell's inequalities, we show that quantum no-cloning theorem can always be certified by Bell's theorem, and this fact in turn reflects that…

We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…

The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…

Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…

It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic…

We recast the quantum no-cloning theorem in a form that preserves spin statistics and apply it to entanglement.

We introduce the concept of cloning for classes of observables and classify cloning machines for qubit systems according to the number of parameters needed to describe the class under investigation. A no-cloning theorem for observables is…

The quantum no cloning theorem is an essential result in quantum information theory. Following this idea, we give a physically natural definition of cloning in the context of classical mechanics using symplectic geometry, building on work…

Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to…

The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound…

Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…

We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well…

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…

We investigate the cases where a set $S$ of states $\{\ket{\psi_i} \}$ cannot be cloned by itself, but is clonable with the help of another system prepared in state $\hat{\rho}_i$. When $S$ is pair-wise nonorthogonal, it is known that one…

It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes,…

It is known that no quantum process can produce a predetermined superposition of unknown arbitrary states. It has already been shown that with some partial information about the states, one can produce with some probability such…