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arXiv:1609.07463 · Physical Review A

Quantum information theory of the Bell-state quantum eraser

Jennifer R. Glick, Christoph Adami

Published Jan 6, 2017• 9 citations
arXivHTMLPDF

Abstract

Quantum systems can display particle- or wavelike properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement can retroactively be made to measure particlelike or wavelike properties (or anything in between). Here we develop a unitary information-theoretic description of this and several related quantum measurement situations that sheds light on the trade-off between the quantum and classical features of the measurement. In particular, we show that both the coherence of the quantum state and the classical information obtained from it can be described using only quantum-information-theoretic tools and that those two measures satisfy an equality on account of the chain rule for entropies. The coherence information and the which-path information have simple interpretations in terms of state preparation and state determination and suggest ways to account for the relationship between the classical and the quantum world.

DOI
10.1103/physreva.95.012105

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Quantum systems can display particle- or wavelike properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement can retroactively be made to measure particlelike or wavelike properties (or anything in between). Here we develop a unitary information-theoretic description of this and several related quantum measurement situations that sheds light on the trade-off between the quantum and classical features of the measurement. In particular, we show that both the coherence of the quantum state and the classical information obtained from it can be described using only quantum-information-theoretic tools and that those two measures satisfy an equality on account of the chain rule for entropies. The coherence information and the which-path information have simple interpretations in terms of state preparation and state determination and suggest ways to account for the relationship between the classical and the quantum world.
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wavelike and particlelike behaviors of single photons, can be complementary in the sense that they are equally real but cannot be observed simultaneously. Quantum measurements, serving as windows providing views into the abstract edifice of quantum theory, are basic tools for manifesting the intrinsic behaviors of quantum objects. However, a quantitative formulation of complementarity that highlights its manifestations in general measurement scenarios remains elusive. Here we develop a general framework for demonstrating quantum complementarity in the form of information exclusion relations (IERs), which incorporates the wave-particle duality relations as particular examples. Moreover, we explore the applications of our theory in entanglement detection and elucidate that our IERs lead to an extended form of entropic uncertainty relations, providing insights into the connection between quantum complementarity and the preparation uncertainty.
This article develops a relational interpretation of the quantum eraser experiment, showing that interference and which‑path information are not intrinsic properties of quantum systems but context‑dependent relational structures. By analyzing the experiment without invoking retrocausality or observer‑dependent collapse, the paper demonstrates that the apparent paradox arises from mixing incompatible informational frames. Interference is recovered when relational coherence is preserved, while its disappearance corresponds to a change in the network of informational relations rather than a physical erasure. The model clarifies the conceptual foundations of the quantum eraser and provides a unified account of interference, measurement, and information flow.
A quantum eraser is proposed that operates in a domain that does not have any classical counterpart. This quantum eraser utilizes the complementary aspect between entanglement and single-partite properties of composite quantum systems. Consequently, in contrast to the duality of visibility and which-path information which establish features of single quantum systems, here, properties of composite quantum systems are considered. In composite quantum systems entanglement might emerge which is of genuine quantum origin. This nonclassical correlation mutually exclude the single-partite properties of the subsystems of the composite quantum system. The single-partite properties can be describes by wave- and particle properties, i.e. the standard wave-particle duality. Remarkably, entanglement can be considered as a resource for observables that do not exist in classical physics. In a bipartite photon system, this observable is the two-particle visibility which describes the phase relations that are shared between both photons of the composite system. The complementary aspect between two-particle visibility and single-partite properties of the subsystems prevents us from the observation of single-partite properties in an entangled biphoton system. The quantum eraser erases the two-partite visibility and retrieves single-partite properties in form of single-particle visibility for both of the two photons. Thus, both observables contain phase information giving rise to interference effects. Here, complementarity is explicitly enforced by entanglement in a quantitative manner.
Abstract Bell inequality violation is a quantitative measurement tool of quantum entanglement between space-like separated particles. Quantum entanglement is the heart of quantum information science, in which the resulting nonlocal correlation between the paired particles is a unique property of quantum mechanics. Over the last few decades, intensive research has been conducted to understand nonlocal quantum features based on the particle nature of quantum mechanics. Here, the role of coincidence detection is analyzed in a simple interferometer using a quantum eraser. To understand the nonlocal quantum feature, coincidence detection between two output photons of an interferometer is coherently analyzed for Bell inequality violations. Based on this understanding, a classical model of the nonlocal quantum correlation is finally presented using coherent light via wave mixing and heterodyne detection.
Quantum Mechanics Particles in the quantum world can also assume wavelike properties. Researchers often use photons to illustrate this particle/wave duality, but electrons interact with each other, which might make them a better choice. Weisz et al. used electrons to create a “quantum eraser” (see the Perspective by Feldman). By taking advantage of the electrons' interaction, the researchers first acquired information about the electrons' path—a process that destroys their wavelike properties. Next, they deliberately erased this information in order to recover the electrons' wave nature. Science , this issue p. [1363][1]; see also p. [1344][2] [1]: /lookup/doi/10.1126/science.1248459 [2]: /lookup/doi/10.1126/science.1255501
Wave-particle duality is a bizarre feature at the heart of quantum mechanics which refers to the mutually exclusive dual attributes of quantum objects as the wave and the particle. Quantum eraser presents a counterintuitive aspect of the wave-particle duality. In this paper, we show that quantum eraser can be quantitatively understood in terms of the recently developed duality-entanglement relation. In other words, we show that wave-particle-entanglement triality captures all the physics of the quantum erasure. We find that a controllable partial erasure of the which-path information is attainable, enabling the partial recovery of the quantum interference and extending the scope of the conventional quantum eraser protocols.