Phase spaces that cannot be cloned in classical mechanics
- URL: http://arxiv.org/abs/2303.00255v3
- Date: Fri, 6 Oct 2023 09:39:46 GMT
- Title: Phase spaces that cannot be cloned in classical mechanics
- Authors: Yuan Yao
- Abstract summary: We show that if $(mathbbR2N, dx_iwedge dy_i)$ can be cloned in our definition, then $M$ must be 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.
- Score: 6.109636030708
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 Fenyes. We observe, following Fenyes, any system with phase space
$(\mathbb{R}^{2N}, dx_i\wedge dy_i)$ can be cloned in our definition. However,
we show that if $(M,\omega)$ 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 $(M, \omega)$ 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.
Related papers
- A Unified Framework for Uniform Signal Recovery in Nonlinear Generative
Compressed Sensing [68.80803866919123]
Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously.
Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples.
We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
arXiv Detail & Related papers (2023-09-25T17:54:19Z) - A Computational Separation Between Quantum No-cloning and
No-teleportation [10.549307055348596]
Two of the fundamental no-go theorems of quantum information are the no-cloning theorem and the no-teleportation theorem.
We give a collection of quantum states and quantum oracles relative to which these states are efficiently clonable but not efficiently teleportable without entanglement.
We show how such states can be used to protect against key exfiltration in cryptography.
arXiv Detail & Related papers (2023-02-03T17:05:38Z) - Optimized Telecloning Circuits: Theory and Practice of Nine NISQ Clones [0.0]
We present results of a of $1 rightarrow 9$ universal, symmetric, optimal quantum telecloning implementation on a cloud accessible quantum computer.
The demonstration of creating $9$ approximate clones on a quantum processor is the largest number of clones that has been generated, telecloning or otherwise.
arXiv Detail & Related papers (2022-10-18T21:12:41Z) - The Asymmetric Quantum Cloning Region [1.2891210250935143]
We study the general case of $1 to N$ asymmetric cloning.
We characterize, for all Hilbert space dimensions and number of clones, the set of all possible clone qualities.
arXiv Detail & Related papers (2022-09-24T12:52:50Z) - A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship
Conjecture [68.8204255655161]
We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold.
We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
arXiv Detail & Related papers (2022-06-17T12:14:33Z) - Quantum Telecloning on NISQ Computers [0.0]
Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning.
NISQ devices can achieve near-optimal quantum telecloning fidelity.
arXiv Detail & Related papers (2022-04-30T01:40:24Z) - The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for
Two-Dimensional Systems [62.997667081978825]
Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation.
We exhaustively study the case of a Hilbert space dimension of $2$.
arXiv Detail & Related papers (2022-04-16T07:03:54Z) - Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.
Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z) - Quantum double aspects of surface code models [77.34726150561087]
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry.
We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
arXiv Detail & Related papers (2021-06-25T17:03:38Z) - Quantum deleting and cloning in a pseudo-unitary system [20.489044283783358]
We investigate the quantum deleting and cloning in a pseudo-unitary system.
We show that it is possible to delete and clone a class of two different and nonorthogonal states.
We simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection.
arXiv Detail & Related papers (2021-03-29T05:59:27Z) - Boundary time crystals in collective $d$-level systems [64.76138964691705]
Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment.
We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
arXiv Detail & Related papers (2021-02-05T19:00:45Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.