Entanglement In Quantum Field Theory Research Articles

Notes on the type classification of von Neumann algebras

This paper provides an explanation of the type classification of von Neumann algebras, which has made many appearances in the recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature between resources that are too technical for the non-expert reader, and resources that seek to explain the broad intuition of the theory without giving precise definitions. Reading this paper will provide you with: (i) an argument for why “factors” are the fundamental von Neumann algebras that one needs to study; (ii) an intuitive explanation of the type classification of factors in terms of renormalization schemes that turn unnormalizable positive operators into “effective density matrices”; (iii) a mathematical explanation of the different types of renormalization schemes in terms of the allowed traces on a factor; (iv) an intuitive characterization of type I and type II factors in terms of their “standard forms”; and (v) a list of some interesting connections between type classification and modular theory, including the argument for why type III1 factors are believed to be the relevant ones in quantum field theory. None of the material is new, but the pedagogy is different from other sources the author has read; it is most similar in spirit to the recent work on gravity and the crossed product by Chandrasekaran, Longo, Penington, and Witten.

How ubiquitous is entanglement in quantum field theory?

How ubiquitous is entanglement in quantum field theory?

Entanglement in quantum field theory via wavelet representations

Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free scalar bosonic and Ising model fermionic QFTs using wavelets. Making use of the orthogonality and self similarity of the wavelet basis functions, we demonstrate some well known relations such as scale dependent subsystem entanglement entropy and renormalization of correlations in the ground state. We also find some new applications of the wavelet transform as a compressed representation of ground states of QFTs which can be used to illustrate quantum phase transitions via fidelity overlap and holographic entanglement of purification.

The large N limit of icMERA and holography

In this work, we compute the entanglement entropy in continuous icMERA tensor networks for large N models at strong coupling. Our results show that the 1/N quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, are related to quantum corrections to the minimal area surface in the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in 1/GN, i.e., at the structure of the quantum corrections in the bulk. The fact that the large N part of the entropy can be always related to the leading area term of the holographic calculation is very suggestive. These results, constitute the first tensor network calculations at large N and strong coupling simultaneously, pushing the field of tensor network descriptions of the emergence of dual spacetime geometries from the structure of entanglement in quantum field theory.

Effective entropy of quantum fields coupled with gravity

Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

Entanglement in composite systems due to external influences

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.

Violation of Cluster Property in Quantum Antiferromagnet

The cluster property is one of fundamental properties in physics. This property means that there are no relations between two events that are sufficiently separated. Because the cluster property is directly connected with entanglement in quantum field theory and in many-body systems, theoretical and experimental progress on entanglement stimulates us to study this property deeply. In this paper we investigate the cluster property in the spin 1/2 XXZ antiferromagnet on the square lattice with an explicitly symmetry breaking interaction of strength g. In this model spontaneous symmetry breaking occurs when the lattice size N is infinitely large. On the other hand, we have to make g zero in order to obtain quantities in the XXZ model with no symmetry breaking interaction. Since some results depend on the sequence of limit operations — and , it is difficult to draw a clear conclusion in these limits. Therefore we study the model with finite g on the finite lattice, whose size N is supposed to be 1020, for our quantitative calculations. Then we can obtain the concrete ground state. In order to study the cluster property we calculate the spin correlation function. It is known that the function due to Nambu-Goldstone mode (gapless mode), which is calculated using linear spin wave theory, satisfies this property. In this paper we show that almost degenerate states also induce the spin correlation. We assume that the spin correlation function in measurements is a sum of the function due to Nambu-Goldstone mode and one due to these degenerate states. Then we examine whether the additional correlation function violates the cluster property or not. Our conclusion is that this function is finite at any distance, which means the violation of the cluster property, and it is of order of . Except for the case of extremely small g, this violation is the fine effect. Therefore the correlation function due to the degenerate states can be observed only when it is larger than the spin correlation function due to Nambu-Goldstone mode. We show that g required for this condition depends on the distance between positions of two spin operators.

Generalized entanglement entropy

We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. The second measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.

Spin operator and entanglement in quantum field theory

Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low energy analysis of entanglement to the ultra-relativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultra-relativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables-type description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all the observable properties of leptons.

Entanglement in Quantum Field Theory: particle mixing and oscillations

The phenomena of particle mixing and flavor oscillations in elementary particle physics are associated with multi-mode entanglement of single-particle states. We show that, in the framework of quantum field theory, these phenomena exhibit a fine structure of quantum correlations, as multi-mode multi-particle entanglement appears. Indeed, the presence of anti-particles adds further degrees of freedom, thus providing nontrivial contributions both to flavor entanglement and, more generally, to multi-partite entanglement. By using the global entanglement measure, based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the multiparticle states of two-flavor neutrinos and anti-neutrinos. A direct comparison with the instance of the quantum mechanical Pontecorvo single-particle states is also performed.

Detecting Vacuum Entanglement in a Linear Ion Trap

We propose and study a method for detecting ground-state entanglement in a chain of trapped ions. We show that the entanglement between single ions or groups of ions can be swapped to the internal levels of two ions by sending laser pulses that couple the internal and motional degrees of freedom. This allows us to entangle two ions without actually performing gate operations. A proof of principle of the effect can be realized with two trapped ions and is feasible with current technology.