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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Squashing models for optical measurements in quantum communication.

Normand J Beaudry¹, Tobias Moroder, Norbert Lütkenhaus

¹Institute for Quantum Computing, University of Waterloo, Waterloo, Canada.

Physical Review Letters

|October 15, 2008

Summary

We developed a method to determine if a measurement can be simplified. The Bennett-Brassard 1984 (BB84) protocol

Area of Science:

Quantum information science
Quantum optics
Quantum measurement theory

Background:

Quantum measurements are typically modeled in infinite-dimensional Fock space.
A simplified model involves signal squashing into a lower-dimensional Hilbert space followed by a target measurement.
This squashing model's applicability to specific quantum protocols is not fully understood.

Purpose of the Study:

To develop a formalism for assessing the validity of squashing models for quantum measurements.
To investigate whether specific quantum cryptography protocols, namely BB84 and the six-state protocol, can be described by a squashing model.
To understand the implications of squashing models for the security proofs of these protocols.

Main Methods:

Formalism development to connect full and target measurement descriptions.

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Application of the formalism to analyze the measurement structures of the BB84 and six-state protocols.

Comparison of the squashing model's applicability between the two protocols.

Main Results:

A formalism was established to analyze squashing models for quantum measurements.
The Bennett-Brassard 1984 (BB84) protocol's measurement was shown to be compatible with a squashing description.
The six-state protocol's measurement was found not to allow a squashing description.

Conclusions:

The BB84 protocol's measurement can be simplified using a squashing model.
This allows security proofs for BB84 to rely on the assumption of at most one forwarded photon by an eavesdropper.
The six-state protocol does not permit such a simplification, impacting its security proof assumptions.