We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.
We discuss the generation of field-induced entanglement between two objects each in a superposition of two trajectories.The objects have currents coupled to local quantum fields, and the currents are evaluated around each trajectory of the objects.The fields have only dynamical degrees of freedom and satisfy the microcausality condition. We find that the superposed state of trajectories cannot be entangled when the objects are spacelike separated.This means that the quantum fields do not generate spacelike entanglement in the superposition of two trajectories of each object.
We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for…
The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein-Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-i…
We consider an entanglement harvesting protocol between two Unruh-deWitt detectors in quantum superpositions of static trajectories in the static de Sitter and thermal Minkowski spacetimes. We demonstrate for the first time that the spatial superposition of each detector's path allows entanglement to be harvested from the quantum field in regimes where it would be otherwise impossible for detectors on classical trajectories. Surprisingly, for detectors on sufficiently delocalised trajectories in a thermal bath, the amount of harvested entanglement grows with the temperature of the field, viola…
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theo…
We study the excess of (Renyi) entanglement entropy in various free field theories for the locally excited states defined by acting with local operators on the ground state. It is defined by subtracting the entropy for the ground state from the one for the excited state. Here the spacetime dimension is greater than or equal to 4. We find a correspondence between entanglement and a probability. The probability with which a quasi-particle exists in a subregion gives the excess of the entropy. We also propose a toy model which reproduces the excess in the replica method. In this model, a quasi-pa…
We establish a one-to-one mapping between entanglement entropy, energy, and temperature (quantum entanglement mechanics) with black hole entropy, Komar energy, and Hawking temperature, respectively. We show this explicitly for 4-D spherically symmetric asymptotically flat and non-flat space-times with single and multiple horizons. We exploit an inherent scaling symmetry of entanglement entropy and identify scaling transformations that generate an infinite number of systems with the same entanglement entropy, distinguished only by their respective energies and temperatures. We show that this sc…
The Bose-Marletto-Vedral (BMV) experiment [3, 4] is a proposal for testing the quantum nature of gravity with entanglement due to Newtonian gravity. This proposal has stimulated controversy on how the entanglement due to Newtonian gravity is related to the essence of quantum gravity and the existence of gravitons. Motivated by this, we analyze the entanglement generation between two charged particles coupled to a photon field. We assume that each particle is in a superposition of two trajectories and that the photon field is initially in a coherent state. Based on covariant quantum electrodyna…
We consider the entanglement entropy in the dS/CFT correspondence.In Einstein gravity on de Sitter spacetime we propose the holographic entanglement entropy as the analytic continuation of the extremal surface in Euclidean anti-de Sitter spacetime.Even though dual conformal field theories for Einstein gravity on de Sitter spacetime have not been known yet,we analyzed the free $Sp(N)$ model dual to Vasiliev's higher spin gauge theory as a toy model.In this model we confirmed the behaviour similar to our holographic result from Einstein gravity.
A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensions $d=2$ and $d=4$ for both the UV divergent and UV finite terms. In dimension $d=4$ an expansion of entanglement entropy in terms of size $L$ of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled CFT, which universally grows as…
This paper revisits standard calculations of free field entanglement entropy in light of the newly developed lattice-continuum correspondence. This correspondence prescribes an explicit method to extract an approximately continuum quantum field theory out of a fully regularized lattice theory. This prescription will here be extended to subregion algebras, and it will be shown how entropies of continuum boson and fermion theories can be computed by working purely with lattice quantities. This gives a clear picture of the origin of divergences in entanglement entropy while also presenting a conc…
The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time-dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence b…
We examine the Hessian potential that derives the flat Minkowski spacetime in $(1+1)$-dimension. The entanglement thermodynamics by the Hessian geometry enables us to obtain the entanglement entropy of a corresponding quantum state by means of holography. We find that the positivity of the entropy leads to the presence of past and future causal cones in the Minkowski spacetime. We also find that the quantum state is equivalent to the thermofield-double state, and then the entropy is proportional to the temperature. The proportionality is consistent with previous holographic works. The present …
The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand…
In a system with chiral topological order, there is a remarkable correspondence between the edge and entanglement spectra: the low-energy spectrum of the system in the presence of a physical edge coincides with the lowest part of the entanglement spectrum (ES) across a virtual cut of the system, up to rescaling and shifting. In this paper, we explore whether the edge-ES correspondence extends to nonchiral topological phases. Specifically, we consider the Wen-plaquette model which has Z_2 topological order. The unperturbed model displays an exact correspondence: both the edge and entanglement s…
We study entanglement entropy for a class of states in quantum field theory that are entangled superpositions of coherent states with well-separated supports, analogous to Einstein-Podolsky-Rosen or Bell states. We calculate the contributions beyond the area law in a simple model. In the case of strongly coupled conformal field theories, we argue that these states are holographically dual to superpositions of bulk geometries. We note that for these states one can use the Ryu-Takayanagi holographic entanglement entropy formula to calculate some terms in the entanglement entropy, but that there …
We give a review of the black-hole/qubit correspondence that incorporates not only the earlier results on black hole entropy and entanglement measures, seven qubits and the Fano plane, wrapped branes as qubits and the attractor mechanism as a distillation procedure, but also newer material including error-correcting codes, Mermin squares, Freudenthal triples and 4-qubit entanglement classification.
String theory provides one of the most deepest insights into quantum gravity. Its single most central and profound result is the gauge/gravity duality, i.e. the emergence of gravity from gauge theory. The two examples of M(atrix)-theory and the AdS/CFT correspondence, together with the fundamental phenomena of quantum entanglement, are of paramount importance to many fundamental problems including the physics of black holes (in particular to the information loss paradox), the emergence of spacetime geometry and to the problem of the reconciliation of general relativity and quantum mechanics. I…
Since euclidean global AdS_2 space represented as a strip has two boundaries, the state / operator correspondence in the dual CFT_1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS_2 x K are described by twisted version of the Hartle-Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual…
