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arXiv:1001.4922 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum entanglement and entropy in particle creation

Shih-Yuin Lin, Chung-Hsien Chou, B. L. Hu

Published Apr 12, 2010• 32 citations
arXivHTMLPDF

Abstract

We investigate the basic theoretical issues in the quantum entanglement of particle pairs created from the vacuum in a time-dependent background field or spacetime. Similar to entropy generation from these processes which depends on the choice of physical variables and how certain information is coarse grained, entanglement dynamics hinges on the choice of measurable quantities and how the two parties are selected as well as the background dynamics of the field or spacetime. We discuss the conditions of separability of quantum states in particle creation processes and point out the differences in how the von Neumann entropy is used as a measure of entropy generation versus for entanglement dynamics. We show by an explicit construction that adoption of a different set of physical variables yields a different entanglement entropy. As an application of these theoretical considerations we show how the particle number and the quantum phase enter the entanglement dynamics in cosmological particle production.

DOI
10.1103/physrevd.81.084018

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We investigate the basic theoretical issues in the quantum entanglement of particle pairs created from the vacuum in a time-dependent background field or spacetime. Similar to entropy generation from these processes which depends on the choice of physical variables and how certain information is coarse grained, entanglement dynamics hinges on the choice of measurable quantities and how the two parties are selected as well as the background dynamics of the field or spacetime. We discuss the conditions of separability of quantum states in particle creation processes and point out the differences in how the von Neumann entropy is used as a measure of entropy generation versus for entanglement dynamics. We show by an explicit construction that adoption of a different set of physical variables yields a different entanglement entropy. As an application of these theoretical considerations we show how the particle number and the quantum phase enter the entanglement dynamics in cosmological particle production.
Quantum entanglement, a defining feature of quantum theory, is generated dynamically by the Schwinger effect—the production of particle-antiparticle pairs from a strong electric field. In this work, we go beyond traditional particle-number analyses to study the quantum entanglement gen- erated in this process. We partition the system into momentum modes and calculate entanglement entropy and logarithmic negativity as functions of time. For a single Sauter pulse, entanglement exhibits a monotonic growth that closely tracks the pair creation process. Strikingly, a train of alternating pulses induces coherent interference, leading to a cumulative enhancement of entan- glement and revealing a clear interplay between successive creation events. Most significantly, we show that the temporal delay (𝑇) between pulses acts as a tunable parameter, controlling the level of entanglement via constructive or destructive interference. This tunability provides a distinct sig- nature of vacuum memory, establishing pair production as a platform for entanglement-controlled strong-field physics.
The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ${\ensuremath{\phi}}^{4}$ theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as ln(m0)\mathrm{ln}({m}_{0})ln(m0​). In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of m0{m}_{0}m0​. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a ${\ensuremath{\phi}}^{r}$ theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where an interaction occurs.
Classical information theory, built on Shannon entropy, and quantum information theory, built on von Neumann entropy, quantify uncertainty and compression properties of probability distributions and density operators. Both are powerful, but both treat information as a property of states of individual systems or ensembles. In this manuscript we argue that entanglement—the pattern of non-classical correlations between systems—is more fundamental than either Shannon or von Neumann information. We motivate this claim with a condensate thought experiment in which many bosons occupy the same single-particle state: Shannon and von Neumann entropies assign them identical information content, yet they can be distinguished by their distinct entanglement histories with external systems. Formally, states with identical marginal density operators but different purifications represent different global information, accessible only through their entanglement structure. Entropic quantities are then seen as coarse-grained summaries of this underlying relational information. We connect this perspective to an entanglement-geometric view of physics, including Entanglement Manifold Cosmology (EMC), in which spacetime and physical “truth” emerge from the geometry of correlations. The goal is an information-theoretic narrative that is rigorous enough for physics and information theory while readable to a non-specialist who is comfortable with basic linear algebra and quantum mechanics.
The Von Neumann entropy of reduced states is a measure of bipartite entanglement. Despite its name, the entanglement entropy cannot by itself be used as a resource for creating thermodynamic heat flows. In order to extract heat from an entangled pure state, it first needs to be converted into a stochastically mixed state by a process of quantum state reduction. Here we show that even in a system with only two degrees of freedom, for which bipartite entanglement is the sole form of entanglement available, the entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one fashion. Moreover, we show that the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction, allows for multiple definitions of entropy. We indicate why quantum state reduction does not allow construction of a perpetuum mobile, despite some measures of entropy evolving non-monotonically during its dynamics. Finally, we relate the different measures of entropy to the information they contain about quantum entanglement and extractable heat, and show that models of quantum state reduction based on physical, correlated stochastic driving forces give rise to observable thermodynamic signatures of quantum state reduction that can be unambiguously distinguished from environment-induced dephasing.
In this thesis we examine a variety of question regarding several quantum information-theoretic concepts as they manifest in the context of relativistic quantum fields. In particular, we study the qualitative and quantitative structure of entanglement (as well as more generalized quantum correlations) in field theory. Primarily we study the nature of vacuum entanglement, but consider spatial correlations in more general field states as well. We also discuss several novel aspects of particle creation phenomena, which generally go hand in hand with the presence of field entanglement. Such investigations are important from two perspectives. First, we gain enlightening new insight into the nature of quantum fields and, therefore, into the fundamental constituents of the matter contained in our universe. Second, we are able to consider the possibility of utilizing the relativistic nature of quantum fields as a resource for quantum technological tasks such as entanglement distribution, information processing, and metrology. \n \nAs a general guiding principle, here we approach such questions from an operational perspective. That is, we focus less on the mathematical facts derivable from a given theory and instead attempt to answer in what concretely physical ways such facts manifest themselves. For example, in what ways can vacuum entanglement actually be experimentally detected and measured, at least in principle? Such an approach allows us to circumvent otherwise problematic interpretational issues. It also lends itself more naturally to the proposal of real world experiments regarding, and utilizations of, the physics being investigated. In this thesis we utilize two models of detection as applied to field theory. \n \nThe first is one that we will develop from scratch and use to great effect in a number of studies; this is the non-perturbative oscillator detector. In this context, a ``detector" is simply some quantum system that is allowed to interact in some way with a quantum field. The response of this system then gives us information about the field properties. Typically such studies are done perturbatively, which presents several severe limitations on what may be investigated. We develop an alternative model, in which the detector is identified as a quantum harmonic oscillator, that allows non-perturbative solutions. We go on to apply this model to a variety of studies. We start by the examining the Unruh effect in a cavity setting. Not only are we able to examine the thermalization behavior of such a detector (which is stronger than what can be achieved perturbatively), we also demonstrate that the Unruh response is largely independent of the cavity boundary conditions, indicating a surprising amount of generality and universality to the phenomenon. We also consider the spacelike extraction of spatial entanglement by a set of such detectors. This includes the harvesting of genuine tripartite entanglement out of the vacuum, as well as the observation that the extractable quantum discord (a generalized measure of quantum correlations) can be greatly amplified by thermal fluctuations in the field, in opposite behavior to entanglement. This calls into question the nature of quantum discord, but also suggests at the possibility of actually using environmental noise as a quantum computational resource. Next, we use the oscillator detector model to great effect by proposing a method of reliably and sustainably generating and distributing entanglement via a cavity field. This protocol is inherently non-perturbative, and we refer to it as entanglement farming. Lastly, we modify the farming scenario to discover a very sensitive resonance effect that generates a large difference in the protocol output due to a minute change in system parameters, including the length of cavity being used. We put this forth as a potential method of quantum seismic metrology. \n \nThe second model that we will consider simply involves performing projective measurements onto a given set of field modes. We will find, however, that such an approach allows us to solve previously intractable problems. In particular, we apply this procedure to the physically sensible choice of localized, positive frequency field modes. Using this model we perform two different studies. In the first, we consider the response of an observer accelerating not through the vacuum state but rather a thermal state. Such a setting has not been (properly) studied previously, due to the computational challenges involved. By applying the localized projective measurement model we are able determine that such an observer sees both an Unruh response from acceleration and a response from the field thermality and that, critically, these responses are distinguishable. We then go on to examine the degradation of quantum correlations between two observers due to the acceleration of one of the observers. This is a prototypical scenario of interest and, by applying realistic measurement assumptions, we obtain results qualitatively different from many previous works on the issue. \n \nIn addition to these models, we question the nature of vacuum entanglement and particle creation by considering an operationally straightforward procedure that greatly demystifies these phenomena and puts them on to solid, physically concrete grounds. This operation is that of very quickly introducing a boundary condition onto one's field, for example by creating a mirror. The real particles generated in this process will then be quantum entangled with each other, even if they are created at spatially separate locations, and this entanglement derives exactly from the previously present vacuum entanglement. Not only does this realization provide an operationally satisfying interpretation of vacuum entanglement, it also suggests a straightforward procedure for its experimental verification. \n \nIn all of this, the computational framework that we will rely upon is that of Gaussian quantum mechanics. This is a restriction of continuous variable quantum mechanics that, while limited in its applicability, provides extremely powerful computational tools in the cases that it may be used. The scenarios of interest in this thesis fall within this category and lend themselves naturally to a Gaussian approach. With this we are able to perform, near trivially, many otherwise intractable studies.