# Quantum cloning and the capacity of the Pauli channel

@inproceedings{Cerf1998QuantumCA, title={Quantum cloning and the capacity of the Pauli channel}, author={Nicolas J. Cerf}, year={1998} }

A family of quantum cloning machines is introduced that produce two approximate copies from a single quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, describing the balance between the quality of the two copies. This also provides an upper bound on the quantum capacity of the Pauli channel with probabilities $p_x$, $p_y$ and $p_z$. The capacity is shown to be vanishing if $(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies…

## 20 Citations

On quantum fidelities and channel capacities

- Computer ScienceIEEE Trans. Inf. Theory
- 2000

It is shown that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel, and that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.

Additive extensions of a quantum channel

- Physics2008 IEEE Information Theory Workshop
- 2008

This work studies extensions of a quantum channel whose one-way capacities are described by a single-letter formula and demonstrates that the key rate of BB84 with one- way post-processing and quantum bit error rate q cannot exceed H(1/2-2q(1-q).

The Quantum Capacity With Symmetric Side Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2008

An upper bound for the quantum channel capacity that is both additive and convex is presented and seems to be quite tight, and for degradable quantum channels, it coincides with the unassisted channel capacity.

Transmitting Quantum Information Reliably across Various Quantum Channels

- Computer Science
- 2013

This dissertation discusses the coding problem from several perspectives, and derives a computationally simple lower bound on the worst case entanglement fidelity of a quantum code, when the truncated recovery map of Leung et al. is rescaled.

Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity

- PhysicsQuantum Inf. Comput.
- 2014

Evaluating the quantum capacity of quantum channels is an important but difficult problem, even for channels of low input and output dimension. Smith and Smolin showed that the quantum capacity of…

The Correlation Conversion property of quantum channels

- Physics, Computer ScienceQuantum Inf. Process.
- 2014

It is proved that the noise transformation of quantum channels that are not able to transmit quantum entanglement can be used to generate distillable (useable)Entanglement from classically correlated input, and is called the Correlation Conversion property of Quantum channels.

Controlling the flow of information in quantum cloners: Asymmetric cloning

- Computer Science
- 1998

A universal cloning network with the help of which asymmetric cloning can be performed is presented and it is shown that the distribution of information at the output of the quantum cloner can be efficiently controlled via preparation of the Quantum Cloner.

Broadcasting of entanglement via orthogonal and non-orthogonal state-dependent cloners

- Computer ScienceQuantum Inf. Process.
- 2020

This work re-conceptualizes the idea of state-dependent quantum cloning machine (SD-QCM), and in that process, it introduces different types of SD-QCMs, namely orthogonal and non-orthogonal cloners, and derives the conditions for which the fidelity of these cloner will become independent of the input state.

The regular histories formulation of quantum theory

- Philosophy
- 2012

It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.

Quantum Cryptography with Several Cloning Attacks

- Computer Science
- 2010

The cloning attack's quantum error is lower than the intercept and resen ds attacks one, which means that the cloning attack is the optimal one for arbitrary number of eavesdroppers.