Classical Spacetimes as Amplified Information in Holographic Quantum Theories

We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes AdS/CFT as a special case, and deduce its consequences. In the first half of the paper, we ask what description of the bulk physics is provided by a holographic state dual to a semiclassical spacetime. In particular, we analyze what portion of the bulk can be reconstructed as spacetime in the holographic theory. The analysis indicates that when a spacetime contains a quasi-static black hole inside a holographic screen, the theory provides a description of physics as viewed from the exterior (though the interior information is not absent). In the second half, we study how and when a semiclassical description emerges in the holographic theory. We find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space. If there are a maximal number of independent microstates, semiclassical operators must be given state-dependently; we elucidate this point using the stabilizer formalism and tensor network models. We also discuss possible implications of the present picture for the black hole interior.Comment: 17 pages, 3 figures; v4: matches published versio

A holographic system for subsea recording and analysis of plankton and other marine particles

We report here details of the design, development, initial testing and field-deployment of the HOLOMAR system for in-situ subsea holography and analysis of marine plankton and nonliving particles. HOLOMAR comprises a submersible holographic camera ("HoloCam") able to record in-line and off-axis holograms at depths down to 100 m, together with specialised reconstruction hardware ("HoloScan") linked to custom image processing and classification software. The HoloCam consists of a laser and power supply, holographic recording optics and holographic plate holders, a water-tight housing and a support frame. It utilises two basic holographic geometries, in-line and off-axis such that a wide range of species, sizes and concentrations can be recorded. After holograms have been recorded and processed they are reconstructed in full three-dimensional detail in air in a dedicated replay facility. A computer-controlled microscope, using video cameras to record the image at a given depth, is used to digitise the scene. Specially written software extracts a binarised image of an object in its true focal plane and is classified using a neural network. The HoloCam was deployed on two separate cruises in a Scottish sea loch (Loch Etive) to a depth of 100 m and over 300 holograms were recorded

Towards a global analysis of generalized parton distributions

We discuss the complexity of GPD phenomenology, comment on the technological needs for a global analysis, and report on model and neural network fits to the photon electroproduction off unpolarized proton. We also point out that Radyushkin's double distribution ansatz is a `holographic' GPD model.Comment: LaTeX, 12 pages, 3 figures, proceedings of the "4th Workshop on Exclusive Reactions at High Momentum Transfer", TJNAF, May 18-21, 2010, plus additional references and footnote

Deep convolutional neural networks and digital holographic microscopy for in-focus depth estimation of microscopic objects

Deep artificial neural network learning is an emerging tool in image analysis. We demonstrate its poten- tial in the field of digital holographic microscopy by addressing the challenging problem of determining the in-focus reconstruction depth of an arbitrary epithelial cell cluster encoded in a digital hologram. A deep convolutional neural network learns the in-focus depths from half a million hologram amplitude images. The trained network correctly determines the in-focus depth of new holograms with high probability, with- out performing numerical propagation. To our knowledge, this is the first application of deep learning in the field of digital holographic microscopy

Tensor network states and geometry

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law -- that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.Comment: 18 pages, 18 figure

Holographic Quantum Circuits from Splitting/Joining Local Quenches

We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially described by time evolutions of boundary surfaces in the bulk AdS. We find that the logarithmic time evolution of entanglement entropy arises from the region behind the Poincare horizon as well as the evolutions of boundary surfaces. In the CFT side, our analysis of entanglement density suggests such a logarithmic growth is due to initial non-local quantum entanglement just after the quench. Finally, by combining our results, we propose a new class of gravity duals, which are analogous to quantum circuits or tensor networks such as MERA, based on the AdS/BCFT construction.Comment: 59 pages, 28 figures; v2: explanations added, minor corrections; v3: eq.(4.25), eq.(4.26) and related contents correcte

Entanglement Wedge Cross Sections Require Tripartite Entanglement

We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well-supported conjectures about the entanglement wedge cross section surface $E_W$. If $E_W$ is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at $\mathcal{O}(\frac{1}{G_N})$. We prove that this implies holographic CFT states must have $\mathcal{O}(\frac{1}{G_N})$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.Comment: 20 pages, 5 figures, comments added in v

Learning to Rank Question Answer Pairs with Holographic Dual LSTM Architecture

We describe a new deep learning architecture for learning to rank question answer pairs. Our approach extends the long short-term memory (LSTM) network with holographic composition to model the relationship between question and answer representations. As opposed to the neural tensor layer that has been adopted recently, the holographic composition provides the benefits of scalable and rich representational learning approach without incurring huge parameter costs. Overall, we present Holographic Dual LSTM (HD-LSTM), a unified architecture for both deep sentence modeling and semantic matching. Essentially, our model is trained end-to-end whereby the parameters of the LSTM are optimized in a way that best explains the correlation between question and answer representations. In addition, our proposed deep learning architecture requires no extensive feature engineering. Via extensive experiments, we show that HD-LSTM outperforms many other neural architectures on two popular benchmark QA datasets. Empirical studies confirm the effectiveness of holographic composition over the neural tensor layer.Comment: SIGIR 2017 Full Pape