arXiv subjects

Gururaj Kadiri

Publications and source records attributed to Gururaj Kadiri.

6 recordsLinked to original sources

arXiv2026

A Unified SU(2) Framework for Vector Beam Transformations and Complex Beam Shaping

We present a constructive framework for designing transformations between structured light fields using birefringent optical elements, formulated in terms of SU(2) operations on polarization. Within this framework, transformations between vector beams are treated as spatially varying SU(2) operations, leading to a direct procedure for designing doubly inhomogeneous waveplates (d-plates) that implement the desired mapping. We identify a condition under which a single element implements a prescribed transformation exactly, including the global phase, and provide an explicit prescription for constructing the corresponding doubly inhomogeneous waveplate (d-plate) when this condition is satisfied, along with its realization using a finite sequence of singly inhomogeneous plates, including a QHQ configuration. Within this formulation, a broad class of problems in structured light can be treated within a single framework, including vector beam transformations, spin-orbital dynamics, and complex beam shaping. Crucially, the same SU(2) operations directly realize quantum channels on the orbital angular momentum degree of freedom, with polarization serving as a physical ancilla. These results establish a unified and explicitly constructive route to complex beam shaping and vector beam transformations based on SU(2) parameter synthesis, and provide a systematic foundation for designing next-generation photonic elements for structured light and spin-orbit information processing.

physics.optics↗

arXiv2026

Quantum State Engineering Under Multiple Expectation-Value Constraints

This work introduces a formulation of quantum state engineering termed expectation-value targeting: the task of preparing a pure state whose expectation values with respect to a prescribed set of observables attain specified targets. This formulation subsumes standard ground-state preparation problems in quantum chemistry and many-body physics, while extending beyond variational energy minimization to multi-constraint state synthesis. The problem amounts to solving a system of nonlinear constraints on an exponentially large state space, for which no general efficient classical approaches are known. Variational quantum algorithms tackle this problem by restricting the search to a low-dimensional parameter space, and relying on classical optimization techniques for solutions. However, these approaches can become extremely ineffective for the present problem, where competing constraints can induce rugged landscapes and vanishing gradients (barren plateaus). Adaptive variational methods, in which the ansatz is constructed iteratively from a pool of candidate operators rather than fixed in advance, have been developed primarily for ground-state preparation. However, we show that the present problem also admits a similar construction. We introduce QUEST (Quantum Unitary Engineering of States to Target), a framework purpose-built for expectation-value targeting, in which the engineered state is constructed as a depth-adaptive sequence of Pauli rotations, with each rotation chosen to descend a sum-of-squared-residuals cost. QUEST provides a constructive route to expectation-value targeting, building the engineered state one Pauli rotation at a time, and establishes adaptive synthesis as a primitive for state preparation under multiple, potentially inconsistent target constraints.

quant-ph↗

arXiv2024

Scouring Parrondo's Paradox in Discrete-Time Quantum Walks

We propose a quantum game based on coin-based quantum walks. Given a quantum walk and a Hermitian operator on the coin-position composite space, winning this game involves choosing an initial coin state such that the given quantum walk leads to a composite state in which the expectation value of the given Hermitian operator is greater than a certain value. Parrondo's paradox is a phenomenon where a combination of losing strategies becomes a winning strategy. We give a deterministic scheme for identifying Parrondo's paradox in our game, in the sense that, given a collection of distinct quantum steps, we identify initial coin states which happen to be losing states for all quantum walks comprising solely of these steps individually, but turn out to be winning states for a quantum walk comprising of all the given steps taken in a sequence. Unlike traditional quantum steps that allow for equal magnitude forward and backward strides based on the outcome of the coin-toss, the steps of the quantum walks employed here, though still contingent upon coin-toss, permit the strides to be of unequal magnitude, and not necessarily in opposite directions. We believe the results presented here will contribute to a deeper understanding of evolution of expectation values of observables in quantum walks, and facilitate the development of novel quantum algorithms.

quant-ph↗

arXiv2022

Steered discrete-time quantum walks for engineering of quantum states

We analyze the strengths and limitations of steered discrete time quantum walks in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the composite space are accessible through quantum walks, even under the most generalized definition of a quantum step, leading to a bifurcation of the composite Hilbert space into "walk-accessible states" and the "walk-inaccessible states". We give an algorithm for generating any walk-accessible state from a simple-to-realize product state, in a minimal number of walk steps, all of unit step size. We further give a prescription towards constructing minimal quantum walks between any pair of such walk-accessible states. Linear optics has been a popular physical system for implementing coin-based quantum walks, where the composite space is built up of spin and orbital angular momenta of light beams. We establish that in such an implementation, all normalized quantum states are "walk-accessible". Furthermore, any generalized quantum step can be implemented upto a global phase using a single q-plate and a pair of homogeneous waveplates. We then give a quantum walk based scheme for realizing arbitrary vector beams, using only q-plates and waveplates.

quant-ph↗

arXiv2021

Realization of doubly inhomogeneous waveplates for structuring of light beams

Waveplates having spatially varying fast-axis orientation and retardance provide an elegant and easy way to locally manipulate different attributes of light beams namely, polarization, amplitude and phase, leading to the generation of exotic structured light beams. The fabrication of such doubly inhomogeneous waveplates (d-plates) is more complex, compared to that of singly inhomogeneous waveplates (s-plates) having uniform retardance, which can be easily fabricated by different means such as photoalignment of liquid crystals, metasurfaces etc. Here, exploiting the SU(2) formalism, we establish analytically that any d-plate can be equivalently implemented using a pair of quarter-wave s-plates and a half-wave s-plate. An important advantage of this method is that it gives the flexibility to realize a whole family of distinct d-plates using the same triplet of s-plates. To underline the scope of this method, we propose novel d-plates for spatially tailoring the phase and complex amplitudes of light beams. Towards complex amplitude shaping, we present a generic method for carving out higher-order eigenmodes of light using a d-plate in conjugation with a polarizer. A generalized q-plate-like gadget, for imparting a polarization-dependent phase profile to a scalar light beam, is proposed as a demonstration of phase-polarization interplay. For these two illustrations, the corresponding three-s-plate gadget is constructed, and its functioning is validated with extensive numerical simulations. The main result and its illustrations are generic and agnostic to the way the s-plates are fabricated and we believe they carry the potential to push the current state of the art in interdisciplinary applications involving structured light beams.

physics.optics↗

arXiv2017

Permutation symmetry and entanglement in quantum states of heterogeneous systems

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed of subsystems having unequal dimensions. Given a tensor product space of $k$ subsystems (of arbitrary dimensions) and a permutation operation $σ$ over $k$ symbols, these states are such that they have identical decompositions (up to an overall phase) in the given tensor product space and the tensor product space obtained by the permuting the subsystems by $σ$. Towards this, we construct a matrix whose action is to simultaneously permute the subsystem label and subsystem dimension of a given state according to permutation $σ$. Eigenvectors of this matrix have the required symmetry. We then examine entanglement of states in the igenspaces of these matrices. It is found that all nonsymmetric eigenspaces of such matrices are completely entangled subspaces, with states being equally entangled in both the given tensor product space and the permuted tensor product space.

quant-ph↗