aqora

What is non-classical about quantum no-cloning?

Ana Belén Sainz

Jun 22, 20203 citations

Cloning in Classical Mechanics

Aaron Fenyes

In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.

arXiv:1010.6103Oct 28, 20101 citation

A General No-Cloning Theorem

Göran Lindblad

Letters in Mathematical PhysicsJan 1, 1999125 citations

Limitations on cloning in classical mechanics

Aaron Fenyes

In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.

Journal of Mathematical PhysicsJan 1, 20127 citations

Optimal cloning and no signaling

Sibasish Ghosh, Guruprasad Kar, Anirban Roy

arXiv:quant-ph/9907001Physics Letters AOct 1, 199926 citations

Phase spaces that cannot be cloned in classical mechanics

Yuan Yao

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 of A. Fenyes, J. Math. Phys. 53, 012902 (2012). We observe, following Fenyes, any system with phase space (R2N,dxi∧dyi) can be cloned in our definition. However, we show that if (M, ω) can be cloned in our definition, then M must be contractible. For instance, this shows the simple pendulum cannot be cloned in Hamiltonian mechanics. We further formulate a robust notion of approximate cloning, and show that if (M, ω) can be approximately cloned, then M is contractible. We give interpretations of our results and in some special cases reconcile our no cloning theorems with the general experience that classical information is clonable. Finally we point to new directions of research, including a connection of our result with the classical measurement problem.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 of A. Fenyes, J. Math. Phys. 53, 012902 (2012). We observe, following Fenyes, any system with phase space (R2N,dxi∧dyi) can be cloned in our definition. However, we show that if (M, ω) can be cloned in our definition, then M must be contractible. For instance, this shows the simple pendulum cannot be cloned in Hamiltonian mechanics. We further formulate a robust notion of approximate cloning, and show that if (M, ω) can be approximately cloned, then M is contractible. We give interpretations of our results and in some special cases reconcile our no cloning theorems with the general experience that classical information is clonable. Finally we point to new directions of research, including a connection of our result with the classical measurement problem.

arXiv:2303.00255Journal of Mathematical PhysicsOct 1, 20231 citation

On classical cloning and no-cloning

Related papers

On classical cloning and no-cloning

Related papers