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arXiv:quant-ph/0309055

Optical telecom networks as weak measurements with post-selection

Nicolas Brunner

Published Sep 5, 2003• 0 citations
arXivHTMLPDF

Abstract

In this work we establish a link between two apparently unrelated subjects: polarization effects in optical fibers and devices, and the quantum theory of weak measurements. We show that the abstract concept of weak measurements followed by post-selection, introduced a decade ago by quantum theorists, naturally appears in the everyday physics of telecom networks.

DOI
10.48550/arxiv.quant-ph/0309055

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In this work we establish a link between two apparently unrelated subjects: polarization effects in optical fibers and devices, and the quantum theory of weak measurements. We show that the abstract concept of weak measurements followed by post-selection, introduced a decade ago by quantum theorists, naturally appears in the everyday physics of telecom networks.
We show that weak measurements with postselection, proposed in the context of the quantum theory of measurement, naturally appear in the everyday physics of fiber optics telecom networks through polarization-mode dispersion (PMD) and polarization-dependent losses (PDL). Specifically, the PMD leads to a time-resolved discrimination of polarization; the postselection is done in the most natural way: one postselects those photons that have not been lost because of the PDL. The quantum formalism is shown to simplify the calculation of optical networks in the telecom limit of weak PMD.
A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.
Post-selection is the selection of a subset of an ensemble based on a measurement on that ensemble. In the last few years, post-selection has taken on new importance as a mechanism to induce the optical nonlinearities required for quantum logic gates. I present experiments and theory that explore post-selection in photonic systems. I then go on to describe an experimental implementation of Hardy's Paradox, which is one of the three great thought-experiments about entanglement and correlations in quantum mechanics (the others being the EPR and GHZ "paradoxes"). In the place of the electron--positron annihilation in the original proposal, I apply, for the first time, a post-selection-based absorptive photon switch that coworkers and I had previously developed. Weak measurement promises to be an important technique for characterizing post-selected quantum systems during their evolution. The technique minimizes disturbance to the system and therefore can be used in situ. In a third experiment, I attempt to resolve a recent debate: Which is more fundamental--complementarity or the uncertainty principle? Specifically, can interference be destroyed by a which-path measurement without transferring momentum to the particle? This question is difficult to investigate as any measurement of the momentum transfer causes collapse, severely disturbing the system. I circumvent this problem with the technique of weak measurement and show that which-path measurements do indeed induce a momentum transfer as required by the uncertainty principle. First, I experimentally demonstrate effective nonlinear absorption between two single photons. I show that this photon-exchange effect can be understood as a post-selection induced nonlinearity similar to the one that occurs in Hong-Ou-Mandel interference. In a fourth experiment, I use the latter theory and return to Hardy's Paradox to perform the first weak measurement of an entangled system. I post-select on the paradoxical measurement result while weakly measuring a set of observables. The results are surprising in that they no longer conflict; they now satisfy a classical-logic truth-table. I then proceed to develop theoretically a new method for performing multiparticle weak measurements that is unique because it does not require single-particle-level interactions. This theory provides new insight into the importance of the imaginary component of the weak measurement result.
This paper presents two unconventional links between quantum and classical physics. The first link appears in the study of quantum cryptography. In the presence of a spy, the quantum correlations shared by Alice and Bob are imperfect. One can either process the quantum information, recover perfect correlations and finally measure the quantum systems; or, one can perform the measurements first and then process the classical information. These two procedures tolerate exactly the same error rate for a wide class of attacks by the spy. The second link is drawn between the quantum notions of “no-cloning theorem” and “weak-measurements with post-selection”, and simple experiments using classical polarized light and ordinary telecom devices.
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being measured. Consideration of the phase is important to clarify its physical interpretation. In classical wave optics, there has long been studies on methods of measuring or retrieving the phase of a wave function. We here present that one of those methods, the analytic phase retrieval based on the properties of entire functions, has a close connection with weak measurements in quantum physics. We explain such a connection for two emblematic optical weak-measurements that have the same mathematical formalism as quantum systems: one is a system for weak measurements of polarized light displacement in a birefringent crystal, and the other is a system for the direct measurement of a wave function by weakly coupling it to a pointer. In those two systems, we show that the pre- and post-selection of polarized light provides a filtering effect similar to that utilized in the analytic phase retrieval.