Abstract

Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.

Highlights

  • We saw that the main challenge in the development of a relativistic quantum information theory (QIT) is the description of measurements/operations in a way that is compatible with locality and causality we explain why the description of measurements in non-relativistic quantum theory cannot be transferred to relativistic quantum field theoretic (QFT)

  • We have argued that the extension of quantum information theory to relativistic systems—including quantum gravity—requires the formulation of a consistent and practicable quantum measurement theory for QFT

  • We presented the challenges that must be overcome by such a theory, and we presented the main ideas of the Quantum Temporal Probabilities (QTP) program that aims to provide such a theory

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Summary

Introduction

The search of gravitational effects in such states is possible, and this raises novel theoretical issues about the interplay of gravity and quantum, especially in relation to locality, causality and information [22,23,24,25] In this field the development of a relativistic QIT is crucial. The QTP method leads to probabilities in which the spacetime point is treated as a random variable, i.e., the observables are time extended This property is absent from past quantum measurement formalisms that were designed for non-relativistic quantum theory.

Current Incompatibilities between QIT and QFT
Problems in Describing Measurements in QFT
Non-Covariance of Projection Rule
Spatial Localization Apparently Conflicts Causality
Ideal Measurements Lead to Violation of Causality
QFT Measurement Models
Key Ideas
The Probability Formulas
Conclusions
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