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Princeton University Press eBooks

1. Elementary Quantum Mechanics

Roland L. Omnes

Published Dec 31, 1994• 0 citations
Publisher

Abstract

5.8 Schematic of the pairs of particles produced by the EPR source with each carrying the same "hidden variables", i.e. outcomes of the measurements of Z and X. 161 5.9 Pairs of particles produced by the EPR source with the same "hidden variables".162 5.10 Schematic of the source creating two particles, one is sent to Alice and one is sent to Bob.

DOI
10.1515/9780691187433-003

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5.8 Schematic of the pairs of particles produced by the EPR source with each carrying the same "hidden variables", i.e. outcomes of the measurements of Z and X. 161 5.9 Pairs of particles produced by the EPR source with the same "hidden variables".162 5.10 Schematic of the source creating two particles, one is sent to Alice and one is sent to Bob.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.
Quantum teleportation requires 2 cbits to be sent from Alice to Bob in order to transmit an {\\em unknown} qubit provided they share an entangled EPR pair. Classical teleportation requires 2.19 cbits to be sent from Alice to Bob in order to transmit a {\\em known} qubit provided they share local hidden variables. We show that there is a simple scheme which requires 1 cbit to be sent from Alice to Bob for transmitting a {\\em known} qubit provided they share an entangled EPR pair. This suggests that the classical teleportation should be compared with the present scheme for comparing the cbit cost (1.19 cbits more) and the use of entanglement versus local hidden variables.
Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.
A novel quantum switch for continuous variables teleportation is proposed. Two pairs of EPR beams with identical frequency and constant phase relation are composed on two beamsplitters to produce two pairs of conditional entangled beams, two of which are sent to two sending stations(Alices) and others to two receiving stations(bobs). The EPR entanglement initionally results from two-mode quadrature squeezed state light. Converting the squeezed component of one of EPR sources between amplitude and phase, the input quantum state at a sender will be reproduced at two receivers in turn. The switching system manipulated by squeezed state light might be developed as a practical quantum switch device for the communication and teleportation of quantum information.