Common notions of entanglement are based on well-separated subsystems. However, obtaining such independent degrees of freedom is not always possible because of physical constraints. In this work, we explore the notion of entanglement in the context of dependent degrees of freedom. As a physically relevant application, we specifically study quantum correlation features for quasiparticle descriptions. Those are paramount for interacting light-matter systems, utilizing excitations of fermion-boson hybrid modes. By comparing independent and dependent degrees of freedom, we uncover that certain states are nonentangled although they would be entangled when only focusing on the common, independent description, and vice versa. Therefore, insight is provided into the resourcefulness of quantum correlations within the rarely discussed context of dependent degrees of freedom for light-matter links in quantum information applications.
Common notions of entanglement are based on well-separated subsystems. However, obtaining such independent degrees of freedom is not always possible because of physical constraints. In this work, we explore the notion of entanglement in the context of dependent degrees of freedom. As a physically relevant application, we specifically study quantum correlation features for quasiparticle descriptions. Those are paramount for interacting light-matter systems, utilizing excitations of fermion-boson hybrid modes. By comparing independent and dependent degrees of freedom, we uncover that certain states are nonentangled although they would be entangled when only focusing on the common, independent description, and vice versa. Therefore, insight is provided into the resourcefulness of quantum correlations within the rarely discussed context of dependent degrees of freedom for light-matter links in quantum information applications.
This paper addresses the following main question: Do we have a theoretical understanding of entanglement applicable to a full variety of physical settings? It is clear that not only the assumption of distinguishability, but also the few-subsystem scenario, are too narrow to embrace all possible physical settings. In particular, the need to go beyond the traditional subsystem-based framework becomes manifest when one tries to apply the conventional concept of entanglement to the physics of matter, since the constituents of a quantum many-body system are indistinguishable particles. We shall discuss here a notion of generalized entanglement, which can be applied to any operator language (fermions, bosons, spins, etc.) used to describe a physical system and which includes the conventional entanglement settings introduced to date in a unified fashion. This is realized by noticing that entanglement is an observer-dependent concept, whose properties are determined by the expectations of a distinguished set of observables without reference to a preferred subsystem decomposition, i.e., it depends on the physically relevant point of view. This viewpoint depends in turn upon the relationship between different sets of observables that determine our ability to control the system of interest. Indeed, the extent to which entanglement is present depends on the observables used to measure a system and describe its states. This represents a most conspicuous advantage as will be highlighted by the condensed-matter application we will discuss.
We introduce a framework to identify where the total correlations and entanglement with a chosen degree of freedom reside within the rest of a system, in the context of bosonic many-body Gaussian quantum systems. Our results are organized into two main propositions. First, for pure Gaussian states, we show that every correlated mode possesses a unique single-degree-of-freedom partner that fully captures its correlations (consisting of entanglement), and we provide an explicit construction of this partner from the complex structure of the system's state. Second, for mixed Gaussian states, we constructively demonstrate that the notion of a partner subsystem splits into two: a correlation partner, which contains all classical and quantum correlations and need not correspond to a single degree of freedom, and an entanglement partner, which is always at most single-mode. Finally, we extend the construction of partners to multi-mode subsystems. Together, these results provide conceptual practical tools to study how bipartite correlations and entanglement are structured and where they can be found in complex Gaussian many-body systems.
The question of whether entanglement between photons is equivalent to entanglement between their characteristic field modes, specifically, the single-particle wavefunctions that are composed and superposed to describe particles in such modes, is a key, open problem concerning multi-partite optical degrees of freedom, and has profound implications for topics ranging from quantum foundations to quantum computation. Here, I offer a fresh, deeper, physical insight into this subtle, albeit enduring, issue by describing a situation in which the entangling interactions between optical modes, namely, the wavefunctions, can be distilled into genuine entanglement between the physical, observable properties of the photons, which are the wavefunctional degrees of freedom. This theoretical observation also highlights the salience of the measurement context, especially, of clearly disambiguating between the choice of the quantum subsystem and the decision to measure an observable along a particular axis of measurement, while quantifying and transforming quantum optical entanglement. This theoretical observation might be applied to formulate a new class of protocols for performing quantum information tasks, using entangled photons within inseparable field modes.
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
Abstract Aside from other puzzling features of entanglement, it has been debated whether a physically meaningful notion of entanglement requires two (or more) particles as carriers of the correlated degrees-of-freedom, or if a single particle could be considered to be entangled as well. While the usefulness of single-boson entanglement has been demonstrated some time ago, the restrictions of superselection rules have previously thwarted attempts at similar arguments for single fermions. In Dasenbrook et al (2016 New J. Phys. 18 043036 ) this obstacle is overcome. The authors propose a scheme for a Bell test on two copies of single-electron states whose entanglement is individually not accessible. The discussed scheme, which makes use of recent progress in electronic quantum optics, provides an experimentally viable and theoretically unambiguous way to assert that certain single-electron states can be considered to be entangled.