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NON-OPTIMAL CLONING OF QUBITS AT A DISTANCE

Iulia Ghiu

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

In contrast to the classical protocol, when one can generate as many copies of a system as one wishes, the no-cloning theorem forbids the perfect cloning of quantum systems. In this paper we present a scheme that enables the imperfect non-optimal copying of a qubit and show how the two nonidentical clones can be distributed to two spatially separated receivers with the help of a nonmaximally entangled channel.

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•Jul 1, 2000•1 citation
In contrast to the classical protocol, when one can generate as many copies of a system as one wishes, the no-cloning theorem forbids the perfect cloning of quantum systems. In this paper we present a scheme that enables the imperfect non-optimal copying of a qubit and show how the two nonidentical clones can be distributed to two spatially separated receivers with the help of a nonmaximally entangled channel.
The main non-classical feature of quantum key distribution (QKD) is that it is characterized by a trade-off relation that limits the information possibly gained by a spy and the quality of the transmission line between the authorized users. In particular, perfect cloning is impossible, due to this trade-off, while optimal imperfect cloning saturates the trade-off relation. We investigate by numerical methods the deep nature of this trade-off relation, in the case of optimal cloning, and find that it reveals a subtle interplay between fidelity and entanglement.
A scheme to create a perfect copy of a three-qubit state with assistance from two preparers is proposed.During the course agreed in the scheme,the sender wish to teleport an unknown three-qubit entangled state which from two preparers to a remote receiver,and then create a perfect copy of the unknown state at her place.The scheme includes two stages.The first stage of the scheme requires usual teleportation.In the second stage,to help the sender realize the quantum cloning,two preparers perform three-qubit projective measurements on their own qubits which is from the sender,then the sender can acquire a perfect copy of the unknown state.The superiority of our protocol is that the rate of success about getting the copy can reach 1.
We consider transmission of classical information through a quantum channel from one sender to several receivers. In contrast to quantum information, classical information carried by two non-orthogonal states of a quantum system can be cloned exactly. This restricts a naive extrapolation of the standard no-cloning theorem. The optimal cloning induces entanglement between clones which increases with non-orthogonality of the states. The capacity of the corresponding quantum channel is considered. As a byproduct of our results, we obtain that for an entangled system with an unknown state there is no transformation which removes the entanglement totally without affecting the corresponding marginal density matrices.
This chapter begins by providing proofs of no-cloning and no-broadcasting theorems. No-cloning theorem makes it possible to detect any eavesdropper on a quantum communication channel. The chapter presents the features of some of the quantum cloning machines. In spite of the no-cloning theorem, it is quite possible to construct a quantum cloning machine which copies an unknown state approximately. A probabilistic cloning machine has been proposed which can succeed only with a probability. When it succeeds it will give a perfect copy. This probabilistic quantum cloning is much useful in studying the B92 quantum key distribution protocol which involves only two non-orthogonal states and we can try to clone it with the largest probability. A telecloning scheme combines cloning with teleportation. A quantum telecloning system for two-level system in which one input is sent to M-receivers has been proposed. The no-hiding theorem is found to have applications in black hole evaporation, quantum teleportation and private quantum channels.
We propose a protocol implementing optimal partial deterministic quantum teleportation for qubits. This is a teleportation scheme realizing deterministically an optimal $1\ensuremath{\rightarrow}2$ asymmetric universal cloning where one imperfect copy of the input state emerges at the sender's station while the other copy emerges at receiver's possibly distant station. The optimality means that the fidelities of the copies saturate the asymmetric cloning inequality. The performance of the protocol relies on the partial deterministic nondemolition Bell measurement that allows us to continuously control the flow of information among the outgoing qubits. We also demonstrate that the measurement is optimal two-qubit operation in the sense of the trade-off between the state disturbance and the information gain.