arXiv subjects

Wen-Cong Gan

Publications and source records attributed to Wen-Cong Gan.

24 records · Page 2Linked to original sources

arXiv2018

Quantum information metric of conical defect

A concept of measuring the quantum distance between two different quantum states which is called quantum information metric is presented. The holographic principle (AdS/CFT) suggests that the quantum information metric $G_{λλ}$ between perturbed state and unperturbed state in field theory has a dual description in the classical gravity. In this work we calculate the quantum information metric of a theory which is dual to a conical defect geometry and we show that it is $n$ times the one of its covering space. We also give a holographic check for our result in the gravity side. Meanwhile, it was argued that $G_{λλ}$ is dual to a codimension-one surface in spacetime and satisfies $G_{λλ}=n_{d}\cdot\mbox{Vol}(Σ_{max})/L^{d}$. We show that the coefficient $n_d$ for conical defect should be rescaled by $n^2$ from the one for AdS. A limit case of conical defect --- the massless BTZ black hole--- is also considered. We show that the quantum information metric of the massless BTZ black hole disagrees with the one obtained by taking the vanishing temperature limit in BTZ black hole. This provides a new arena in differiating the different phases between BTZ spacetime and its massless cousin.

hep-th↗

arXiv2017

Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime

For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can increase the uncertainty in quantum measurement. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying quantum uncertainty relations. Here we demonstrate that the bounds of the entropic uncertainty relations, in the presence of memory, can be formulated in terms of the Holevo quantity, which limits how much information can be encoded in a quantum system. Specifically, we considered two examples with Dirac fields, near the event horizon of a Schwarzschild black hole, the Holevo bound provides a better bound than the previous bound based on the mutual information. Furthermore, if the memory moves away from the black hole, the difference between the total uncertainty and the Holevo bound remains a constant, not depending on any property of the black hole.

quant-ph↗

arXiv2017

Holography as deep learning

Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method \cite{CT}. The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this essay, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of deep neural network is of Ryu-Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum field theory.

gr-qc↗

arXiv2017

Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in $AdS_{2+1}$ are explored and several important properties are obtained. These properties allow us, via the RFS/HC duality, to obtain a set of remarkable identities of the reduced fidelity susceptibility, which may have significant implications for our understanding of the reduced fidelity susceptibility. Moreover, utilizing these properties and the recent proposed diagnostic tool based on the fidelity susceptibility, experimental verification of the RFS/HC duality becomes possible.

hep-th↗

arXiv2016

Emergent geometry, thermal CFT and surface/state correspondence

We study a conjectured correspondence between any codimension two convex surface and a quantum state (SS-duality for short). By generalizing thermofield double formalism to continuum version of the multi-scale entanglement renormalization ansatz (cMERA) and using the SS-duality, we show that thermal geometries naturally emerge as a result of hidden quantum entanglement between boundary CFTs. We therefore propose a general framework to emerge the thermal geometry from CFT at finite temperature. As an example, the case of $2d$ CFT is considered. We calculate its information metric and show that it is either BTZ black hole or thermal AdS as expected.

hep-th↗

arXiv2016

Thermal geometry from CFT at finite temperature

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of $2d$ CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

hep-th↗