arXiv subjects

Kallol Sen

Publications and source records attributed to Kallol Sen.

At least 19 recordsLinked to original sources

arXiv2025

Temporal steering of entanglement decay with single-shot control

Entanglement in open quantum systems can vanish abruptly through entanglement sudden death (ESD) under dissipative evolution, posing a challenge for quantum technologies. Here, we show that the timing of a single local unitary operation can deterministically steer the trajectory of entanglement decay. This introduces temporal steering of dissipative quantum dynamics as a control resource. We develop a time-dependent open-system framework in which a time-shift operator generates a family of effective conditional maps parametrized by $x \in [0,1]$, connecting independent and correlated amplitude damping. Within this framework, we derive analytic conditions for ESD and show that a single intermediate local $\sigma_x$ operation can avoid, delay, or hasten ESD by redirecting the dissipative trajectory rather than modifying the environment. We further prove that this single-shot protocol is optimal within a broad class of local control strategies. Experimentally, a displaced-Sagnac interferometer realizes the correlated-damping-like regime and, for the first time in one photonic platform, demonstrates avoidance, delay, and hastening of the separability transition. Our results establish temporal steering of open-system dynamics as a practical paradigm for decoherence control, and demonstrate operational advantages in use cases such as teleportation, illustrating that in dissipative quantum systems knowing \textit{when} to act can be as important as knowing \textit{what} operation to perform.

quant-ph↗

arXiv2023

Exploring $2d$ localization with a step dependent coin

We generalize the coin operator of \cite{Zahed_2023}, to include a step dependent feature which induces localization in $2d$. This is evident from the probability distributions which can be further used to categorize the localized walks. Localization is also evident from the entropic measures. We compute and compare three distinct measures (a) Shannon Entropy in the position and coin space, (b) Entanglement entropy between position and spin space, and (c) Quantum Relative Entropy which is a POVM of density operators of the step dependent and step independent coins. Shannon Entropy and Entanglement Entropy are periodic and bounded functions of the time steps. The zeros of Shannon and Entanglement entropies signify a complete localization of the wave-function. The Quantum Relative Entropy and Quantum Information Variance exhibit a similar periodic feature with a zero minima where the step dependent and step independent walks coincide. Finally, we compute the numerical localization length (inverse of the Lyapunov Exponent) for the step dependent coin as a function of energy and compare with an approximate perturbative computation, where we put the step dependent coin as a perturbation in the background of a step independent coin. In both the instances, we find that the localization length peaks at approximately the same positions in the momentum space.

quant-ph↗

arXiv2023

Quantum-walk search in motion

In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify the marked nodes as well as identify the correct chronological ordering between the marked nodes, if any. To address this limitation, we explore a potential extension of the algorithm by introducing additional quantum states to label the marked nodes. The labels resolve the ambiguity of simultaneous amplification of the marked nodes. Additionally, by associating the label states with a chronological ordering, we can extend the algorithm to track a moving particle on a two-dimensional surface. Our algorithm efficiently searches for the trajectory of the particle and is supported by a proposed quantum circuit. This concept holds promise for a range of applications, from real-time object tracking to network management and routing.

quant-ph↗

arXiv2023

Complexity for one-dimensional discrete time quantum walk circuits

We compute the complexity for the mixed state density operator derived from a one-dimensional discrete-time quantum walk (DTQW). The complexity is computed using a two-qubit quantum circuit obtained from canonically purifying the mixed state. We demonstrate that the Nielson complexity for the unitary evolution oscillates around a mean circuit depth of $k$. Further, the complexity of the step-wise evolution operator grows cumulatively and linearly with the steps. From a quantum circuit perspective, this implies a succession of circuits of (near) constant depth to be applied to reach the final state.

quant-ph↗

arXiv2023

A simple coin for a $2d$ entangled walk

We analyze the effect of a simple coin operator, built out of Bell pairs, in a $2d$ Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the {\it Entangling Power} of the coin operator. Secondly, we compute the {\it Generalized Relative Rényi Entropy} between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the {\it Entangling Power} and {\it Generalized Relative Rényi Entropy} behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the $2d$ DQRW into two $1d$ massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

quant-ph↗

arXiv2021

Notes on AdS-Schwarzschild eikonal phase

We consider the eikonal phase associated with the gravitational scattering of a highly energetic light particle off a very heavy object in AdS spacetime. A simple expression for this phase follows from the WKB approximation to the scattering amplitude and has been computed to all orders in the ratio of the impact parameter to the Schwarzschild radius of the heavy particle. The eikonal phase is related to the deflection angle by the usual stationary phase relation. We consider the flat space limit and observe that for sufficiently small impact parameters (or angular momenta) the eikonal phase develops a large imaginary part; the inelastic cross-section is exactly the classical absorption cross-section of the black hole. We also consider a double scaling limit where the momentum becomes null simultaneously with the asymptotically AdS black hole becoming very large. In the dual CFT this limit retains contributions from all leading twist multi stress tensor operators, which are universal with respect to the addition of higher derivative terms to the gravitational lagrangian. We compute the eikonal phase and the associated Lyapunov exponent in the double scaling limit.

hep-th↗

arXiv2020

Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories

We extend the analysis of \cite{Chowdhury:2019hns} to study the Regge trajectories of the Mellin amplitudes of the $0-$ and $1-$ magnon correlators of the generalized Fishnet theory in $d$ dimensions and one type of correlators of chiral fishnet theory in $4$ dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our $d$ dimensional results reduce to previously known results in $d=4$ for 0-magnon and 1- magnon. As a non trivial check, we show that the results for 1-magnon correlator in $d=8$, when evaluated using the exact techniques in \cite{Chowdhury:2019hns, Korchemsky:2018hnb} are in perfect agreement with our $d$ dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator $\langle{\rm Tr}[ϕ_1(x_1)ϕ_1(x_2)]{\rm Tr}[ϕ_1^\dagger(x_3)ϕ_1^\dagger(x_4)]\rangle$ using the techniques developed in this paper. Since this correlator has two couplings $κ$ and $ω$, we have obtained closed-form results in the limit $κ\to 0, ω\to 0$ with $κ/ω$ held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.

hep-th↗

arXiv2019

Relating diagrammatic expansion with conformal correlator expansion

In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis. This basis can be utilized to expand, I) the four point function of scalars near the Wilson-Fisher fixed point in $d=4-ε$ as in \cite{Alday:2017zzv} and II) integrals for loop diagrams for massless $ϕ^4$ theory in position space in four dimensions. This suggests that a linear combination of one expansion can be recast in terms of a linear combination of the other. As a by-product, we also derive the Mellin space representation for the twist-2 higher spin conformal blocks. We also discuss the higher derivative contact terms in the present scenario.

hep-th↗

arXiv2019

Positive geometry in the diagonal limit of the conformal bootstrap

We consider the diagonal limit of the conformal bootstrap in arbitrary dimensions and investigate the question if physical theories are given in terms of cyclic polytopes. Recently, it has been pointed out that in $d=1$, the geometric understanding of the bootstrap equations for unitary theories leads to cyclic polytopes for which the faces can all be written down and, in principle, the intersection between the unitarity polytope and the crossing plane can be systematically explored. We find that in higher dimensions, the natural structure that emerges, due to the inclusion of spin, is the weighted Minkowski sum of cyclic polytopes. While it can be explicitly shown that for physical theories, the weighted Minkowski sum of cyclic polytopes is not a cyclic polytope, it also turns out that in the large conformal dimension limit it is indeed a cyclic polytope. We write down several analytic formulae in this limit and show that remarkably, in many cases, this works out to be very good approximation even for $O(1)$ conformal dimensions. Furthermore, we initiate a comparison between usual numerics obtained using linear programming and what arises from positive geometry considerations.

hep-th↗

arXiv2019

On the Regge limit of Fishnet correlators

We study the Regge trajectories of the Mellin amplitudes of the $0-,1-$ and $2-$ magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for $0$ and $1$ magnon correlators, the Regge poles can be exactly determined as a function of coupling, $2$-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation.

hep-th↗

arXiv2019

Polology of Superconformal Blocks

We systematically classify all possible poles of superconformal blocks as a function of the scaling dimension of intermediate operators, for all superconformal algebras in dimensions three and higher. This is done by working out the recently-proven irreducibility criterion for parabolic Verma modules for classical basic Lie superalgebras. The result applies to correlators for external operators of arbitrary spin, and indicates presence of infinitely many short multiplets of superconformal algebras, most of which are non-unitary. We find a set of poles whose positions are shifted by linear in $\mathcal{N}$ for $\mathcal{N}$-extended supersymmetry. We find an interesting subtlety for 3d $\mathcal{N}$-extended superconformal algebra with $\mathcal{N}$ odd associated with odd non-isotropic roots. We also comment on further applications to superconformal blocks.

hep-th↗

arXiv2019

Resummation at finite conformal spin

We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion formula of Caron-Huot and the integral (Mellin) representation of conformal blocks, we show that the contribution from individual exchanges to anomalous dimensions and corrections to the OPE coefficients for "double-twist" operators $[\mathcal{O}_1\mathcal{O}_2]_{Δ,J}$ in $s-$channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic {\it wrt} space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.

hep-th↗

arXiv2018

Anomalous dimensions at finite conformal spin from OPE inversion

We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as from the integral (viz. Mellin) representation of the conformal blocks. The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform. We evaluate the contributions of scalar and spin exchanges in the $t-$channel exactly, in terms of higher order Hypergeometric functions. These relate to a particular exchange of conformal spin $β=Δ+J$ in the $s-$channel through the inversion formula. Our exact results reproduce the special cases for large spin anomalous dimension and OPE coefficients obtained previously in the literature.

hep-th↗

arXiv2018

First-order conformal perturbation theory by marginal operators

We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space formalism with the dimensional regularization, we explicitly check that the deformed and renormalized two and three point functions are conformally invariant.

hep-th↗

arXiv2017

Conformal Bootstrap in Mellin Space

We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mellin representation of CFT amplitudes. We employ exchange Witten diagrams with built in crossing symmetry as our basic building blocks rather than the conventional conformal blocks in a particular channel. Demanding consistency with the operator product expansion (OPE) implies an infinite set of constraints on operator dimensions and OPE coefficients. We illustrate the power of this method in the epsilon expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and, strikingly, obtaining OPE coefficients to higher orders in epsilon than currently available using other analytic techniques (including Feynman diagram calculations). Our results enable us to get a somewhat better agreement of certain observables in the 3d Ising model, with the precise numerical values that have been recently obtained.

hep-th↗

arXiv2016

A Mellin space approach to the conformal bootstrap

We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of $CFT_d$ four point functions and expands them in terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about $d=4$. We reproduce Feynman diagram results for operator dimensions to $O(ε^3)$ rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at $ε=1$). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.

hep-th↗

arXiv2016

On critical exponents without Feynman diagrams

In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-ε$ dimensions up to $O(ε^2)$.

hep-th↗

arXiv2016

Assembling topological insulators with lasers

Despite the realizations of spin-orbit (SO) coupling and synthetic gauge fields in optical lattices, the associated time-reversal symmetry breaking, and 1D nature of the observed SO coupling pose challenges to obtain intrinsic $Z_2$ topological insulator. We propose here a model optical device for engineering intrinsic $Z_2$ topological insulator which can be easily set up with the existing tools. The device is made of a periodic lattice of quantum mechanically connected atomic wires (dubbed SO wires) in which the laser generated SO coupling ($α_{\bf k}$, with ${\bf k}$ being the momentum) is reversed in every alternating wires as $\pmα_{\bf k}$. The associated small Zeeman terms are also automatically reversed in any two adjacent SO wires, which allow to effectively restore the global time-reversal (TR) symmetry. Therefore, the two SO wires serve as the TR partner to each other which is an important ingredient for $Z_2$ topological insulators according to the Kane-Mele model. These properties ensure a non-trivial $Z_2$ invariant topological insulator phase with protected edge states. We also discuss that a non-local current measurement can be used to detect the chiral edge states.

cond-mat.mes-hall↗