arXiv subjects

Pratik Nandy

Publications and source records attributed to Pratik Nandy.

25 records · Page 2Linked to original sources

arXiv2022

Balanced Partial Entanglement and Mixed State Correlations

Recently in Ref.\cite{Wen:2021qgx}, one of the authors introduced the balanced partial entanglement (BPE), which has been proposed to be dual to the entanglement wedge cross-section (EWCS). In this paper, we explicitly demonstrate that the BPE could be considered as a proper measure of the total intrinsic correlation between two subsystems in a mixed state. The total correlation includes certain crossing correlations which are minimized on some balance conditions. By constructing a class of purifications from Euclidean path-integrals, we find that the balanced crossing correlations show universality and can be considered as the generalization of the Markov gap for canonical purification. We also test the relation between the BPE and the EWCS in three-dimensional asymptotically flat holography. We find that the balanced crossing correlation vanishes for the field theory invariant under BMS$_3$ symmetry (BMSFT) and dual to the Einstein gravity, indicating the possibility of a perfect Markov recovery. We further elucidate these crossing correlations as a signature of tripartite entanglement and explain their interpretation in both AdS and non-AdS holography.

hep-th↗

arXiv2021

Bath deformations, islands and holographic complexity

Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the AdS-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.

hep-th↗

arXiv2021

Eigenstate capacity and Page curve in fermionic Gaussian states

Capacity of entanglement (CoE), an information-theoretic measure of entanglement, defined as the variance of modular Hamiltonian, is known to capture the deviation from the maximal entanglement. We derive an exact expression for the average eigenstate CoE in fermionic Gaussian states as a finite series, valid for arbitrary bi-partition of the total system. Further, we consider the complex SYK$_2$ model in the thermodynamic limit and we obtain a closed-form expression of average CoE. In this limit, the variance of the average CoE becomes independent of the system size. Moreover, when the subsystem size is half of the total system, the leading volume-law coefficient approaches a value of $π^{2}/8 - 1$. We identify this as a distinguishing feature between integrable and quantum-chaotic systems. We confirm our analytical results by numerical computations.

quant-ph↗

arXiv2021

Partial islands and subregion complexity in geometric secret-sharing model

We compute the holographic subregion complexity of a radiation subsystem in a geometric secret-sharing model of Hawking radiation in the "complexity = volume" proposal. The model is constructed using multiboundary wormhole geometries in AdS$_{3}$. The entanglement curve for secret-sharing captures a crossover between two minimal curves in the geometry apart from the usual eternal Page curve present for the complete radiation entanglement. We compute the complexity dual to the secret-sharing minimal surfaces and study their "time" evolution. When we have access to a small part of the radiation, the complexity shows a jump at the secret-sharing time larger than the Page time. Moreover, the minimal surfaces do not have access to the entire island region for this particular case. They can only access it partially. We describe this inaccessibility in the context of "classical" Markov recovery.

hep-th↗

arXiv2021

Capacity of Entanglement in Local Operators

We study the time evolution of the excess value of capacity of entanglement between a locally excited state and ground state in free, massless fermionic theory and free Yang-Mills theory in four spacetime dimensions. Capacity has non-trivial time evolution and is sensitive to the partial entanglement structure, and shows a universal peak at early times. We define a quantity, the normalized "Page time", which measures the timescale when capacity reaches its peak. This quantity turns out to be a characteristic property of the inserted operator. This firmly establishes capacity as a valuable measure of entanglement structure of an operator, especially at early times similar in spirit to the Renyi entropies at late times. Interestingly, the time evolution of capacity closely resembles its evolution in microcanonical and canonical ensemble of the replica wormhole model in the context of the black hole information paradox.

hep-th↗

arXiv2021

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in $d$-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

hep-th↗

arXiv2020

Renormalized Circuit Complexity

We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. The optimized ST iteration order is correlated with the error tolerance and plays the role of an anti-de Sitter (AdS) radial coordinate. The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given.

hep-th↗