Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in arbitrary dimensions. We obtain analytical closed-form results for the two-point function, Wilson loop and entanglement entropy for strip geometries in the finite-temperature field-theory dual. According to the duality, these are given by the area of minimal surfaces of different dimension in the gravity background. Our analytical results involve generalised hypergeometric functions. We show that they reproduce known numerical results to great accuracy. Our results allow to identify new physical behaviour: for instance, we consider the entanglement density, i.e. the difference of entanglement entropies at finite and vanishing temperature divided by the volume of the entangling region. For field theories of dimension seven or higher, we find that the entanglement density displays non-monotonic behaviour as function of l · T , with l the strip width and T the temperature. This implies that the area theorem, proven for RG flows in general dimensions, does not apply here. This may signal the emergence of new degrees of freedom for AdS Schwarzschild black holes in eight or more dimensions.

/pdf/non-local-observables-at-finite-temperature-in-ads-cft-37jq8mff2o.pdf

5 – Quantum Information

Non-local observables at finite temperature in AdS/CFT

Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in arbitrary dimensions. We obtain analytical closed-form results for the two-point function, Wilson loop and entanglement entropy for strip geometries in the finite-temperature field-theory dual. According to the duality, these are given by the area of minimal surfaces of different dimension in the gravity background. Our analytical results involve generalised hypergeometric functions. We show that they reproduce known numerical results to great accuracy. Our results allow to identify new physical behaviour: For instance, we consider the entanglement density, i.e. the difference of entanglement entropies at finite and vanishing temperature divided by the volume of the entangling region. For field theories of dimension seven or higher, we find that the entanglement density displays non-monotonic behaviour as function of l*T, with l the strip width and T the temperature. This implies that the area theorem, proven for RG flows in general dimensions, does not apply here. This may signal the emergence of new degrees of freedom for AdS Schwarzschild black holes in eight or more dimensions.

Here, the existence of at least one positive radial solution of the Nonlinear nonhomogeneous Neumann problem − Δ H n u + R ( ξ ) u = a ( | ξ | H n ) | u | q − 2 u 1 + | u | q − p − b ( | ξ | H n ) ...

Nonlinear nonhomogeneous Neumann problem on the Heisenberg group

We study the effect of disorder and dephase in transmission of a CdS quantum wire using the Green’s function technique. Our results show that the transmission decreases with the increasing disorder strength. The resistance of a CdS quantum wire with phase-breaking scattering only increases with increasing dephasing. Obtained results show that the drain current of a CdS quantum wire with inelastic scattering by phonons with energy $$\hbar \omega = 30$$
 meV decreases with the increasing disorder strength. Moreover, our theoretical results are independently supported by simulations of CdS disordered quantum wires based on a tight-binding model.

Low-temperature transport in CdS disordered quantum wires: dephasing

Nowadays, quantum computing is a very promising technology. Quantum computers, rather than using merely 1 s or 0 s, execute calculations based on the probability of an object's condition before it is measured, allowing them to process exponentially more data than traditional computers. A bit is a single state, such as on or off, up or down, 1 or 0. Instead, operations in quantum computing utilise the quantum state of an item to produce a qubit. These are the undefined qualities of an object before they are discovered, such as an electron's spin or a photon's polarisation. Several firms are releasing tools for quantum computing practice. One of the tools we'll use to implement our quantum programming is IBM's experience. It also aids in the execution of our programs on real quantum devices. We'll look at the IBM Q experience, circuit composer and building circuits with quantum lab notebooks in this chapter. The dashboard containing the fundamental information is introduced in the IBM Q experience. The user interface for learning quantum circuits, qubits and the gates that are used to perform operations on each qubit is outlined in circuit composer. Creating quantum circuits using quantum lab notebooks shows how to build circuits with the Notebook with Qiskit that comes pre-installed on IBM Quantum Experience. 

5 – Quantum Information

Citations

Non-local observables at finite temperature in AdS/CFT

Non-local observables at finite temperature in AdS/CFT

Nonlinear nonhomogeneous Neumann problem on the Heisenberg group

Low-temperature transport in CdS disordered quantum wires: dephasing

Exploring IBM Quantum Experience

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