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arXiv:2006.13246

Holography from Decoherence and Entanglement

Josh Kirklin

Published Jun 23, 2020• 2 citations
arXivHTMLPDF

Abstract

We describe an explicit mechanism for the emergence of a dynamical holographic bulk from the structure of entanglement in a quantum state. We start with a generic system in complete isolation, assuming it has a classical limit involving coherent states. Then we entangle it with another system of that kind, and subject the pair to a decohering process. We make a number of broadly applicable and physically reasonable assumptions about this setup. First, we assume that the states selected by the decoherence (called pointer states) have the same local symmetries as the isolated systems, in a sense which is made precise. We also assume that the modular Hamiltonians of pointer states scale inversely with Planck's constant, so that the pointer states are highly entangled in the classical limit. Finally, we require the timescale of decoherence to scale in a certain way with Planck's constant, so that decoherence happens very frequently in the classical limit, but not too frequently. Given these assumptions, we demonstrate that the semiclassical evolution of the system is dominated by a certain dynamical generalisation of Uhlmann holonomy. We construct a coherent state path integral for this evolution, showing that the semiclassical fields evolve in a spacetime with one more dimension than the isolated case. The additional dimension is generated by modular flow.

DOI
10.48550/arxiv.2006.13246

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We describe an explicit mechanism for the emergence of a dynamical holographic bulk from the structure of entanglement in a quantum state. We start with a generic system in complete isolation, assuming it has a classical limit involving coherent states. Then we entangle it with another system of that kind, and subject the pair to a decohering process. We make a number of broadly applicable and physically reasonable assumptions about this setup. First, we assume that the states selected by the decoherence (called pointer states) have the same local symmetries as the isolated systems, in a sense which is made precise. We also assume that the modular Hamiltonians of pointer states scale inversely with Planck's constant, so that the pointer states are highly entangled in the classical limit. Finally, we require the timescale of decoherence to scale in a certain way with Planck's constant, so that decoherence happens very frequently in the classical limit, but not too frequently. Given these assumptions, we demonstrate that the semiclassical evolution of the system is dominated by a certain dynamical generalisation of Uhlmann holonomy. We construct a coherent state path integral for this evolution, showing that the semiclassical fields evolve in a spacetime with one more dimension than the isolated case. The additional dimension is generated by modular flow.
We further develop perturbative methods used to calculate entanglement entropy (EE) away from an interacting CFT fixed point. At second order we find certain universal terms in the renormalized EE which were predicted previously from holography and which we find hold universally for relevant deformations of any CFT in any dimension. We use both replica methods and direct methods to calculate the EE and in both cases find a non-local integral expression involving the CFT two point function. We show that this integral expression can be written as a local integral over a higher dimensional bulk modular hamiltonian in an emergent AdS space-time. This bulk modular hamiltonian is associated to an emergent scalar field dual to the deforming operator. We generalize to arbitrary spatially dependent couplings where a linearized metric emerges naturally as a way of efficiently encoding the field theory entanglement: by demanding that Einstein’s equations coupled to the bulk scalar field are satisfied, we show that EE can be calculated as the area of this metric. Not only does this show a direct emergence of a higher dimensional gravitational theory from any CFT, it allows for effective evaluation of the the integrals required to calculate EE perturbativly. Our results can also be interpreted as relating the non-locality of the modular hamiltonian for a spherical region in non-CFTs and the non-locality of the holographic bulk to boundary map.
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large NNN limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large NNN limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large NNN theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).
Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states. The coarse-graining procedure involves identifying degrees of freedom entangled at short distances and disentangling them. This is manifested in the bulk by a flow equation that generates a codimension-1 object, which we refer to as the holographic slice. We generalize the earlier classical construction to include bulk quantum corrections, which naturally involves the generalized entropy as a measure of the number of relevant boundary degrees of freedom. The semiclassical coarse graining results in a flow that approaches quantum extremal surfaces such as entanglement islands that have appeared in discussions of the black hole information paradox. We also discuss the relation of the present picture to the view that the holographic dictionary works as quantum error correction.
This study investigates quantum holography, emphasizing its capability to conduct holographic imaging without the requirement for first-order coherence—a limitation of classical physics. By harnessing quantum entanglement, where image data is embedded in the phase correlation of polarization-entangled photon pairs and spread across the transverse spatial dimension, quantum holography enhances imaging performance. This technique not only improves resolution for polarization-sensitive phase objects but also provides resilience against stochastic phase fluctuations and uncontrolled ambient light, offering significant tangible benefits compared to conventional holography. Additionally, its integration with quantum tomography enables precise analysis of multi-dimensional hyper-entangled states, advancing quantum state analysis. Although current challenges remain, such as extended acquisition times due to technological constraints, ongoing advancements in faster, more affordable sensors are expected to address these issues. As a result, quantum holography is poised to have broad applications in biological imaging, sensing, and the exploration of complex high-dimensional quantum states. These developments position quantum holography as a crucial technology in the future of quantum optical communication and information processing, driving innovation and opening new avenues in these fields.
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Within this framework, theories are conceptual constructs applying to models generated in the phenomenal world within limited contexts.The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases of quantum mechanical states (entanglement). The quantum correlations are shared globally in the process of environment-induced decoherence whereby locally generated correlations are removed, the removal being especially manifest in the case of systems that appear as classical ones, in which case the process is almost instantaneous, being, in all likelihood, driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining its finest details, since Planck scale physics remains an obscure terrain. In other words, the present day quantum theory holds within a limited context set by the Planck scale.
Flat space holography is an open and hard problem existing several different approaches, which may finally turn out to be consistent with each other, in the literature to tackle it. Focusing on how bulk emergent spacetime is encoded in quantum information of null boundaries, we choose a specific toy model called the flat3_33​/BMSFT model, which conjectures the duality between boundary BMS3_33​ invariant field theory and bulk quantum gravity in 3D asymptotic flat spacetimes (AFS), to explore. Aiming to find an entanglement wedge like quantity for single interval and a connected entanglement wedge for multi-intervals in flat3_33​/BMSFT model, we explore the bulk causality structures related to the holographic swing surface proposal through both boundary and bulk local modular flow, make a corresponding decomposition of the global Minkowski spacetime and look at the entanglement phase transition. As a byproduct, we solve the problem about the existence of partial entanglement entropy (PEE) correspondence in this model which is a bit nontrivial due to the unusual behavior of boundary modular flow in BMS3_33​ field theory. Among the literature considering quantum information aspects of flat3_33​/BMSFT model, there are several substantial, unusual but overlooked phenomena which need to be emphasized and revisited to gain more deserved attention. Thus another motivation of this paper is to find where these unusual phenomena come from, and physically show in a manifest way what they may imply. After reading we hope readers can feel sincerely what we present about the above mentioned second aim is more valuable than the mathematical results in the present paper.