arXiv subjects

Aatif Kaisar Khan

Publications and source records attributed to Aatif Kaisar Khan.

6 recordsLinked to original sources

arXiv2026

Detector-Frame Quantum Limits for Heterodyne Timing in Relativistic Optical Links

Long-baseline optical links for space interferometry and satellite quantum networks rely on heterodyne phase tracking under Doppler motion and gravitational frequency shifts. These relativistic shifts can generate large detector-frame beat-frequency offsets over finite readout windows and thereby constrain the temporal precision of front-end phase readout. We develop a detector-frame framework for this problem using an effective two-mode signal--local-oscillator model in which relativistic motion rescales the local-oscillator frequency. Within this setting we derive closed-form Mandelstam--Tamm and Margolus--Levitin bounds for representative Gaussian resources and connect global state distinguishability with the operational precision of heterodyne phase tracking. In the bright-local-oscillator regime we identify a geometric--operational mismatch: the joint optical state can evolve on arbitrarily short global timescales while the relevant information rate is set by the measured detector record. Combining this result with an open-loop transient-acquisition analysis, we show that white phase noise and relativistic beat-frequency drift that is approximately constant over the acquisition window generate a cube-root scaling benchmark for the optimal pre-lock open-loop integration window and the minimum residual phase error. These results establish detector-frame benchmarks for quantum-limited heterodyne timing in relativistic optical links and clarify how global dynamical bounds enter task-restricted continuous optical measurements.

quant-ph↗

arXiv2025

Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification

Timing and phase resolution in satellite QKD, kilometre-scale gravitational-wave detectors, and space-borne clock networks hinge on quantum-speed limits (QSLs), yet benchmarks omit relativistic effects for coherent and squeezed probes. We derive first-order relativistic corrections to the Mandelstam-Tamm and Margolus-Levitin bounds. Starting from the Foldy-Wouthuysen expansion and treating $-p^{4}/(8 m^{3} c^{2})$ as a harmonic-oscillator perturbation, we propagate Gaussian states to obtain closed-form QSLs and the quantum Cramér-Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an $ε^{2} t^{2}$ phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ($ε\approx 1.5\times 10^{-10}$) in a $5.4\,\mathrm{T}$ Penning trap, read out with $149\,\mathrm{GHz}$ quantum-limited balanced homodyne, should reveal this drift within $\sim 15\,\mathrm{min}$ -- within known hold times. These results benchmark relativistic corrections in continuous-variable systems and point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.

quant-ph↗

arXiv2025

Consequences of Godel Theorems on Third Quantized Theories Like String Field Theory and Group Field Theory

The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a theory is described on the configuration space of fields rather than spacetime, which is a third quantized theory. So, both string theory and group field theory are third-quantized theories. Thus, using axioms of string field theory, we motivate similar axioms for group field theory. Then, using the structure of these axioms for string field theory and group field theory, we identify general features of axioms for any such third quantized theory of quantum gravity. Thus, we show that such third-quantized theories of quantum gravity can be formulated as formal axiomatic systems. We then analyze the consequences of Gödel theorems on such third quantized theories. We thus address problems of consistency and completeness of any third quantized theories of quantum gravity.

hep-th↗

arXiv2024

Implications of Tarski's Undefinability Theorem on the Theory of Everything

The Theory of Everything ($S_{\text{ToE}}$) seeks to unify all fundamental forces of nature, including quantum gravity, into a single theoretical framework. This theory would be defined internally using a set of axioms, and this paper proposes a set of axioms for any such theory. Furthermore, for such a theory, all scientific truth would be defined internally as consequences derivable from the rules of such a theory. This paper then examines the implications of Tarski's undefinability theorem on scientific truths derived from such axioms. We demonstrate that Tarski's theorem imposes limitations on any such formal system $S_{\text{ToE}}$. However, we also argue that the Lucas-Penrose argument suggests that non-algorithmic understanding can transcend these formal limitations.

physics.hist-ph↗

arXiv2024

Effects of underlying topology on quantum state discrimination

In this work, we show that quantum state discrimination can be modified due to a change in the underlying topology of a system. In particular, we explicitly demonstrate that the quantum state discrimination of systems with underlying discrete topology differs from that of systems with underlying continuous topology. Such changes in the topology of a spacetime can occur in certain quantum gravity approaches. In fact, all approaches to quantum gravity can be classified into two types: those with underlying continuous topology (such as string theory) and those with an underlying discrete topology (such as loop quantum gravity). We demonstrate that the topology of these two types of quantum gravity approaches has different effects on the quantum state discrimination of low-energy quantum systems. We also show that any modification of quantum mechanics, which does not change the underlying topology, does not modify quantum state discrimination.

gr-qc↗

arXiv2023

Deformation of Nanowires and Nanotubes

In this article, we have investigated the consequences of the next to the leading order correction to the effective field theory of nanostructures. This has been done by analyzing the effects of deformed Heisenberg algebra on nanowires and nanotubes. We first deform the Schrodinger equation with cylindrical topology. Then specific solutions to the deformed Schrodinger equation with different boundary conditions are studied. These deformed solutions are used to investigate the consequences of the deformation on the energy of nanowires and nanotubes.

cond-mat.mes-hall↗