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arXiv:quant-ph/0305085

Teleportation Protocols Requiring Only One Classical Bit

Subhash C. Kak

Published May 15, 2003• 7 citations
arXivHTMLPDF

Abstract

The standard protocol for teleportation of a quantum state requires an entangled pair of particles and the use of two classical bits of information. Here, we present two protocols for teleportation that require only one classical bit. In the first protocol, chained XOR operations are performed on the particles before one of them is removed to the remote location where the state is being teleported. In the second protocol, three entangled particles are used.

DOI
10.48550/arxiv.quant-ph/0305085

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The standard protocol for teleportation of a quantum state requires an entangled pair of particles and the use of two classical bits of information. Here, we present two protocols for teleportation that require only one classical bit. In the first protocol, chained XOR operations are performed on the particles before one of them is removed to the remote location where the state is being teleported. In the second protocol, three entangled particles are used.
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.
In this work, we consider two stages one qubit quantum teleportation protocol via an arbitrary entangled two qubits state. In the first stage, Alice use XOR gate and computational basis measurement, while for the second stage, Alice use Hadamard gate and another computational basis measurement. Alice sent measurement result to Bob via one classical bit each. As the result, we show that this teleportation can has unit fidelity if the channel used has non-zero two terms and maximally entangled. Then the protocol is applicable if the channel is one of four Bell's state.
We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
We propose two schemes for teleporting an arbitrary three-particle state.In the first scheme,a two-particle state and a three-particle entangled state (both non-maximally entangled states)are used as quantum channels,while in the second scheme,three non-mnaximally entangled particle pairs are employed as quantum channels.We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations.Their success probabilities and the classical communication costs are different.
With three pairs of entangled particles as the quantum channel, we present a scheme for preparing remotely a three-particle entangled state. One different point between remote state preparation and quantum teleportation is that we assume Alice starts with complete classical knowledeg of the state but Bob doesn't. Then the state wanted will be got through a series of operation. Eventually, a conclusion that remote state preparation needs less classical resource than quantum teleportation can be made.
We propose two schemes for teleporting an arbitrary three-particle state. In the first scheme, a two-particle state and a three-particle entangled state (both non-maximally entangled states) are used as quantum channels, while in the second scheme, three non-maximally entangled particle pairs are employed as quantum channels. We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations. Their success probabilities and the classical communication costs are different.