Elsevier

Physics Letters A

Volume 270, Issue 5, 5 June 2000, Pages 239-244
Physics Letters A

Towards quantifying non-local information transfer: finite-bit non-locality

https://doi.org/10.1016/S0375-9601(00)00315-7Get rights and content

Abstract

The advent of Bell's inequalities provoked the possibility that entangled quantum phenomena are non-local in nature. Since teleportation only requires two bits, we investigated whether non-local correlations can be further quantified in terms of finite information. The EPR–Bell cosine correlation is reproduced exactly using on average 1.48 bits.

Section snippets

Background

Since the advent of Bell's inequalities and the subsequent experimental evidence, it is speculated by some that there exists in nature information transfer across large distances that occurs faster then the speed of light, and perhaps, instantaneously. While such information transfer may occur internally to elementary particles, it is widely accepted that internal information transfer cannot be utilized to develop a classical signaling system that transmits external information instantaneously.

Non-local internal information transfer

There have been numerous studies regarding quantum information. However, the problem presented in this Letter does not appear to have been solved (related results were obtained independently by Brassard et al. [2] discussed in Section 5). In [3] the question of how many bits are required to transmit a qubit reliably is examined. The approach appears to be based on an approximation, and a fidelity or accuracy is defined. In [4] several related information quantities are addressed.

The issue of

Internal information transfer models

We will examine the amount of information that is transferred via models that allow for the non-local transfer of hidden information. Consider the EPR experiment shown in Fig. 1. There is a quantity ΛI that characterizes the initial state. Experimenter A has a Stern–Gerlach measurement apparatus oriented at θa which records A=1 or −1 and experimenter B has a similar apparatus specified by θb. The source is positioned closer to A than B. Two entangled spin 1/2 particles will be assumed to be

Issues of Lorentz invariance and simultaneity

It has been noted in several papers such as [8] among others that realistic theories either require a preferred frame of reference or will give rise to well-known causal paradoxes. This has implications on causality when considering multi-simultaneity experiments [9]. There are several types of causality violations that can emerge when considering such models. We will consider two types. The first type of violation is that the experimenter can observe what he is about to do. The second

Further work

There is significant work remaining to be done. In this Letter, the EPR experiment with two particles was analyzed. It would also be useful to analyze the teleportation problem that requires three particles. If it can be proven that the amount of non-locality required to replicate the teleportation experiments is greater than 2 bits, then teleportation must be non-local (considered over the set of FBNL models). If, on the other hand, the amount of non-locality required is less than or equal to

Acknowledgements

The author thanks Louis Sica for many valuable insights. Thanks also to Richard Cleve, Mort Rubin, and Alain Tapp, for discussions on this work.

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Paper presented at the Physics of Quantum Electronics Conference, January 3–7, 1999.

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