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Quantum Measurements are Disturbing: Experiments studying the role of disturbance in postselected metrology, quantum pigeonholes, and entangled sheep

Noah Lupu-Gladstein

Published Nov 1, 2024• 0 citations
OpenAlex

Abstract

This thesis details two experiments and one theoretical manuscript that explore the nature of measurement disturbance in quantum mechanics. The first experiment exploits measurement disturbance to enhance measurement precision by two orders of magnitude, and in principle even more. The second experiment investigates a paradox where three quantum pigeons seem to occupy two pigeonholes without any pair belonging to the same hole. It finds that measurement disturbance accounts for some, but not all of the counter-intuitive phenomena at play in the paradox. The final manuscript develops a new theoretical framework for studying quantum measurement and disturbance from the viewpoint of quantum agents. Our framework reveals how agents endowed with quantum memories might view measurement not as a stochastic collapse, but as a continuous flow of quantum information.

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This thesis details two experiments and one theoretical manuscript that explore the nature of measurement disturbance in quantum mechanics. The first experiment exploits measurement disturbance to enhance measurement precision by two orders of magnitude, and in principle even more. The second experiment investigates a paradox where three quantum pigeons seem to occupy two pigeonholes without any pair belonging to the same hole. It finds that measurement disturbance accounts for some, but not all of the counter-intuitive phenomena at play in the paradox. The final manuscript develops a new theoretical framework for studying quantum measurement and disturbance from the viewpoint of quantum agents. Our framework reveals how agents endowed with quantum memories might view measurement not as a stochastic collapse, but as a continuous flow of quantum information.
The pigeonhole principle: "If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole," is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.
This thesis presents the results of a series of four photonic experiments on the topic of quantum measurement. The first two experiments relate to quantum metrology, and the use of quantum states to increase the precision of measurements beyond what is possible with classical systems; first to detect and characterize decoherence, and then in the context of quantum imaging. The third experiment studies a fundamental question in quantum mechanics: "How much must a quantum system be disturbed by a measurement?". We use weak measurement to confirm a recent theoretical result, showing that if a particle's state is already sufficiently uncertain we can perform a measurement with very little disturbance -- contrary to common explanations of Heisenberg's uncertainty principle. The fourth experiment falls in the category of quantum computation. In quantum mechanics having multiple copies of an identical system allows us to extract more information than we can extract from a single copy (since quantum mechanics allows each system to be measured only once before collapsing). We present and experimentally implement a quantum algorithm to compress all of the "extractable information" present in an ensemble of identical copies of quantum bits into exponentially fewer quantum bits. The research presented here samples from a variety of topics in quantum information, showing in several contexts how fascinating quantum effects can be exploited to gain a "quantum enhancement".To enable these experiments two sources of entangled photons were built, and "hybrid" quantum systems (encoding information in multiple degrees of freedom of a photon) were used to implement quantum circuits. This thesis will present the details of one of these sources (a novel and practical source of entangled N00N states), which was used in a four-photon quantum metrology experiment. The other, more standard, source of polarization-entangled photon pairs will only briefly be reviewed to leave room for the discussion of hybrid quantum logic.
We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre- and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counterintuitive phenomena, we employ a we employ variable-strength nonlocal measurements. As we decrease the measurement strength, we find the violation of the sum rule decreases, yet the pigeonhole principle remains violated. In the weak limit, the sum rule is restored due to the cancellation between two weak values with equal and opposite imaginary parts. We observe the same kind of cancellation at higher measurement strengths, thus raising the question: do strong measurements have imaginary parts?
Abstract Quantum mechanics is usually formulated with an implicit assumption that agents who can observe and interact with the world are external to it and have a classical memory. However, there is no accepted way to define the quantum–classical cut and no a priori reason to rule out fully quantum agents with coherent quantum memories. In this work, we introduce an entirely quantum notion of measurement, called a sensation, to account for quantum agents that experience the world through quantum sensors. Sensations eschew probabilities and instead describe a deterministic flow of quantum information. We quantify the information gain and disturbance of a sensation using concepts from quantum information theory and find that sensations always disturb at least as much as they inform. Viewing measurements as sensations could lead to a new understanding of quantum theory in general and to new results in the context of quantum networks.
It was recently argued that the pigeonhole principle, which states that if three pigeons are put into two pigeonholes then at least one pigeonhole must contain more than one pigeon, is violated in quantum systems [Proc. Natl. Acad. Sci. USA 113, 532 (2016)]. An experimental verification of this effect was recently reported [Proc. Natl. Acad. Sci. USA 116, 1549 (2019)]. In another recent experimental work, it was argued that two entities were observed to exchange properties without meeting each other [Nat. Commun. 11, 3006 (2020)]. Here we describe all these proposals and experiments as simple quantum interference effects where no such dramatic conclusions appear. Besides demystifying some of the conclusions of the cited works, we also present physical insights for some interesting behaviors present in these treatments. For instance, we associate the anomalous particles behaviors in the quantum pigeonhole effect to a quantum interference of force.
Quantum mechanics is usually formulated with an implicit assumption that agents who can observe and interact with the world are external to it and have a classical memory. Quantum measurement theory has consequently been formally defined with such external agents in mind, and its predictions match our classical experience. There is however no accepted way to define the quantum-classical cut and (if quantum theory is universal) no a priori reason to rule out fully quantum agents with coherent quantum memories. In this work we extend the definition of measurement to account for observers with quantum memories who need not experience the world in the way we do. We define measurements without probabilities, and show that information gain and uncertainty can still be quantified in a meaningful way. The results demonstrate how quantum agents observe the world in a way that cannot be accounted for in the usual language of observables and POVMs. This approach to measurements could lead to a new understanding of quantum theory in general and to new results in the context of quantum networks.