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arXiv:cs/0603045

Information and Errors in Quantum Teleportation

Balaji Nedurumalli

Published Mar 10, 2006• 1 citation
arXivHTMLPDF

Abstract

This article considers the question of the teleportation protocol from an engineering perspective. The protocol ideally requires an authority that ensures that the two communicating parties have a perfectly entangled pair of particles available to them. But this cannot be unconditionally established to the satisfaction of the parties due to the fact that an unknown quantum state cannot be copied. This supports the view that quantum information cannot be treated on the same basis as classical information.

DOI
10.48550/arxiv.cs/0603045

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This article considers the question of the teleportation protocol from an engineering perspective. The protocol ideally requires an authority that ensures that the two communicating parties have a perfectly entangled pair of particles available to them. But this cannot be unconditionally established to the satisfaction of the parties due to the fact that an unknown quantum state cannot be copied. This supports the view that quantum information cannot be treated on the same basis as classical information.
Abstract Chapter 14 discusses the quantum communication protocol called quantum teleportation, which uses the quantum correlations in an entangled particle pair shared between two observers to transmit the information stored in the (unknown) quantum state of a target system from one of the observers to the other. After reviewing the theoretical basics we showcase some of the important experimental demonstrations of teleportation. We then turn to more general protocols related to teleportation such as entanglement swapping, and the general formalism of isometries, before inspecting the option of delayed-choice entanglement swapping. In the light of these findings we compare teleportation to classical information transfer and inspect the related dense-coding protocol. Finally, we give an overview of basic quantum key distribution protocols is given, including the Bennett-Brassard-84 protocol based on conjugate coding and the entanglement-based Ekert-91 protocol
Quantum teleportation allows one to transmit an arbitrary qubit from point A to point B using a pair of (pre-shared) entangled qubits and classical bits of information. The conventional protocol for teleportation uses two bits of classical information and assumes that the sender has access to only one copy of the arbitrary qubit to be sent. Here, we ask whether we can do better than two bits of classical information if the sender has access to multiple copies of the qubit to be teleported. We place no restrictions on the qubit states. Consequently, we propose a modified quantum teleportation protocol that allows Alice to reset the state of the entangled pair to its initial state using only local operations. As a result, the proposed teleportation protocol requires the transmission of only one classical bit with a probability greater than one-half. This has implications for efficient quantum communications and the security of quantum cryptographic protocols based on quantum entanglement.
What is proposed here is a simple modication in the quantum protocol [1] for achieving instantaneous teleportation of arbitrary quantum state from Alice to Bob even when Bob is several light years away. This modied quantum protocol is constructed by adding a step the in the celebrated quantum teleportation protocol [1]. It consists of the action of a unitary operator to be performed by Alice on the qubits in her possession before she does the Bell basis measurement. It is important to note that the existing quantum teleportation protocol [1] requires certain classical communication between the participants, Alice and Bob, and we are going to eliminate this classical communication through our modification. In the existing protocol [1] Alice requires sending the classical bits generated during her Bell basis measurement over a classical channel to Bob for Bob to use these classical bits to determine the exact recovery operation to be performed on the qubit(s) in his possession for creating the exactly identical copy of unknown quantum state that was with Alice and got destroyed during her Bell basis measurement. Alice cannot send the classical bits she obtained to Bob with the speed faster than that of light since it is the well known experimentally veried universal upper limit on the speed. We show that by incorporating suitable unitary operation to be performed by Alice on her qubits before the Bell basis measurement the requirement of the transmission of classical bits by Alice to Bob for the creation of the unknown quantum state by Bob at his place can be completely eliminated. Our modification in the teleportation protocols [1], [2] thus clearly demonstrates the enormous advantage of remaining in the quantum regime and avoiding the requirement of any classical communication for the teleportation of the quantum states.
We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an unknown state with minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation, and in the second stage the preparer disentangles the leftover entangled states by a single-particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. Our protocol produces clones and complement clones of unknown qubit each with a probability 12\frac{1}{2}21​ and clones of real qubit with unit probability.