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arXiv:quant-ph/0610081

Teleporting a qubit a la Everett

George Svetlichny

Published Oct 10, 2006• 1 citation
arXivHTMLPDF

Abstract

If both Alice and Bob have access to a two-qubit "background state" then, by simulating Everett's many worlds interpretation of measurement, Alice can teleport a qubit to Bob, each using fixed unitaries. The Everett picture unifies unitaries, measurements, and classical communication into just unitaries, provided there are background states shared by all parties. We review some of the literature on this theme and point out an additional fact: If Bob has access to only one of the background qubits, teleportation is still possible by Alice sending Bob one classical bit of information gained from a measurement of the other qubit.

DOI
10.48550/arxiv.quant-ph/0610081

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If both Alice and Bob have access to a two-qubit "background state" then, by simulating Everett's many worlds interpretation of measurement, Alice can teleport a qubit to Bob, each using fixed unitaries. The Everett picture unifies unitaries, measurements, and classical communication into just unitaries, provided there are background states shared by all parties. We review some of the literature on this theme and point out an additional fact: If Bob has access to only one of the background qubits, teleportation is still possible by Alice sending Bob one classical bit of information gained from a measurement of the other qubit.
Summary form only given. Characterizing the entanglement of a general bipartite quantum system is a difficult problem. Most measures involve difficult extremizations and their physical motivation is not always clear. In this paper we propose an experimental measure of entanglement based on a modified version of the familiar teleportation protocol of Bennett et al. (1993). Briefly, teleportation traditionally involves two parties, Alice and Bob. Initially, Alice has a qubit in an unknown quantum state which she would like to communicate to Bob and Bob has two qubits in an entangled Einstein-Podolsky-Rosen (EPR) pair. To accomplish this transfer, Bob shares one qubit of his EPR pair with Alice. She then performs a joint measurement or Bell measurement on her two qubits and relays this information back to Bob over a classical channel. Bob then uses the outcome of Alice's Bell measurement to transform his qubit, with a local unitary transformation, into the original quantum state, always with a fidelity of one.
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.
In this article, the authors have discussed the Alice and Bob experimental set-up for the quantum teleportation, giving a detailed step-by step mathematical explanation of each unit. Quantum teleportation of a qubit requires the creation of an entangled quantum state between the sender’s (Alice) and the receiver’s (Bob) shared quantum state/s. At the end of this experiment, actual measurements of the Alice’s share of quantum information are to be taken and shared with Bob via a classical communication channel. The teleportation is expected to open up a whole new regime of quantum communication, data encryption to be one of its applications.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
Alice and Bob each have a qubit, and they would like to perform a two-qubit gate on them with the assistance of Charlie. The action of this gate depends on a parameter, which either Charlie knows, will receive later as classical information, or is encoded in a program state. We discuss both the case in which Alice and Bob send Charlie their qubits, which he entangles with his state, and the case where Alice and Bob use teleportation to entangle their states with Charlie's state. All of these procedures depend on the ability of Alice and Bob to apply local correction operations that depend on the results of measurements that Charlie makes, and we discuss under what conditions such operations are possible.
A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.