Abstract The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl–Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg–Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and NC QM for Gaussian Wigner functions, our results suggest a feasible interpretation for the NC continuous variable quantum cloning given in terms of quantum teleportation protocols.Abstract The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl–Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg–Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and NC QM for Gaussian Wigner functions, our results suggest a feasible interpretation for the NC continuous variable quantum cloning given in terms of quantum teleportation protocols.

arXiv:1801.03767Journal of Physics A Mathematical and TheoreticalJul 25, 20197 citations

Quantum Mechanics on Phase Space

Franklin E. Schroeck

Springer eBooksJan 1, 1996166 citations

Quantum mechanics on phase space

Nicolaas P. Landsman

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern PhysicsJan 1, 19996 citations

Phase-space approach to continuous variable quantum teleportation

Masashi Ban

The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the $s$ -parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan $P$ function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where ${\mathcal{F}}_{c}$ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the $s$-parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan $P$ function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where ${\mathcal{F}}_{c}$ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.

Physical Review AMay 17, 200437 citations

Quantum Mechanics on Phase Space

Manuel Gadella

Springer eBooksJan 1, 19933 citations

The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the

s

-parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan

P

function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where

{\mathcal{F}}_{c}

is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.