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Information propagation and entanglement generation between two Unruh-DeWitt detectors

Mathieu Cliche

Published Jul 23, 2010• 3 citations
OpenAlex

Abstract

The setup in which two quantum systems, Alice and Bob, communicate using \nbosonic field quanta can be viewed as a prototype for wireless quantum communication. \nIn this thesis we focus on the most basic case, where Alice and Bob \nare modeled as Unruh-DeWitt detectors, i.e., as two-level quantum \nsystems that interact locally through a scalar quantum field. Our aim is to study how information propagation and entanglement generation between the two detectors are impacted by both relativity and by the unavoidable noise that is due to the quantum fluctuations of the field. \n \nWe start by studying information propagation between the two detectors. Concretely, we construct and study the information-theoretic quantum channel, ξ, i.e., the completely positive trace preserving map between the input density matrix ϱ, in which Alice prepares her detector for the emission, and the output density matrix ϱ '=ξ(ϱ) of Bob's detector at a later time. We confirm that the classical as well as the quantum channel capacity are strictly zero to all orders in perturbation theory for spacelike separations. \n \nWe then study entanglement generation between the two detectors. Specifically, we discuss how two Unruh-DeWitt detectors can extract entanglement from the vacuum. We show that the detectors can naturally and instantaneously become entangled through a Casimir-Polder effect. We then analyze the impact of various additions to this setup, such as the presence of a weak gravitational field, the presence of boundary conditions in the field, the presence of a weak classical potential, etc.

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The setup in which two quantum systems, Alice and Bob, communicate using \nbosonic field quanta can be viewed as a prototype for wireless quantum communication. \nIn this thesis we focus on the most basic case, where Alice and Bob \nare modeled as Unruh-DeWitt detectors, i.e., as two-level quantum \nsystems that interact locally through a scalar quantum field. Our aim is to study how information propagation and entanglement generation between the two detectors are impacted by both relativity and by the unavoidable noise that is due to the quantum fluctuations of the field. \n \nWe start by studying information propagation between the two detectors. Concretely, we construct and study the information-theoretic quantum channel, ξ, i.e., the completely positive trace preserving map between the input density matrix ϱ, in which Alice prepares her detector for the emission, and the output density matrix ϱ '=ξ(ϱ) of Bob's detector at a later time. We confirm that the classical as well as the quantum channel capacity are strictly zero to all orders in perturbation theory for spacelike separations. \n \nWe then study entanglement generation between the two detectors. Specifically, we discuss how two Unruh-DeWitt detectors can extract entanglement from the vacuum. We show that the detectors can naturally and instantaneously become entangled through a Casimir-Polder effect. We then analyze the impact of various additions to this setup, such as the presence of a weak gravitational field, the presence of boundary conditions in the field, the presence of a weak classical potential, etc.
Setups in which a system Alice emits field quanta that a system Bob receives are prototypical for wireless communication and have been extensively studied. In the most basic setup, Alice and Bob are modeled as Unruh-DeWitt detectors for scalar quanta, and the only noise in their communication is due to quantum fluctuations. For this basic setup, we construct the corresponding information-theoretic quantum channel. We calculate the classical channel capacity as a function of the spacetime separation, and we confirm that the classical as well as the quantum channel capacity are strictly zero for spacelike separations. We show that this channel can be used to entangle Alice and Bob instantaneously. Alice and Bob are shown to extract this entanglement from the vacuum through a Casimir-Polder effect.
We study the full entanglement dynamics of two uniformly accelerated Unruh-DeWitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back-to-back in the field vacuum. For two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances, though each detector never enters the other's light cone in this setup. In the weak coupling limit, this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors. Once entanglement is created it lasts only a finite duration, and always disappears at late times. Prior result by Reznik [B. Reznik, Found. Phys. 33, 167 (2003).] derived using the time-dependent perturbation theory with extended integration domain is shown to be a limiting case of our exact solutions at some specific moment. In the strong coupling and high acceleration regime, vacuum fluctuations experienced by each detector locally always dominate over the cross correlations between the detectors, so entanglement between the detectors will never be generated.
We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional space-time, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation, even when the detectors are separated acausally, while we observe no violation of the Bell--CHSH inequality. In the case of the Minkowski vacuum, in particular, we find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future.
Abstract The quantum channel between two particle detectors provides a prototype framework for the study of wireless quantum communication via relativistic quantum fields. In this article we calculate the classical channel capacity between two Unruh–DeWitt detectors arising from couplings within the perturbative regime. To this end, we identify the detector states which achieve maximal signal strength. We use these results to investigate the impact of relativistic effects on signaling between detectors in inertial and uniformly accelerated motion which communicate via a massless field in Minkowski spacetime.
The degradation of quantum resources due to environmental noise is a fundamental challenge in quantum information science. In relativistic settings, this noise is intrinsically linked to vacuum fluctuations. Here, we investigate this connection using a model of two Unruh-DeWitt detectors interacting with a scalar field in Minkowski spacetime. Specifically, we focus on Bell nonlocality, quantum coherence, the nonlocal advantage of quantum coherence, and measured uncertainty, examining their dependence on the detector-field energy ratio, the inter-detector distance, and the initial state parameter. Notably, our central finding is that vacuum fluctuations are the primary mechanism of decoherence. Moreover, while spatial separation induces decoherence, all quantum resources converge to a non-zero steady state at large distances, confirming the robustness of nonlocality. These insights provide a deeper understanding of quantumness in a relativistic framework and may contribute to the ongoing discussion on the black hole information paradox.
Two entangled two-level Unruh-DeWitt detectors, which are in rest, spontaneously lose entanglement when at least one of them is not isolated from the environment quantum fields. For eternal interaction between the detectors and environment, the spontaneous emission from the detectors' exited states and vacuum fluctuations of field influence this negative effect. Consequently, it suggests that two entangled qubits become less communicated during their free fall towards the black hole horizon.