arXiv subjects

Shashaank Khanna

Publications and source records attributed to Shashaank Khanna.

6 recordsLinked to original sources

arXiv2026

Accelerating Fourier--Motzkin elimination: redundancy removal and the choice of variable elimination order

Fourier-Motzkin elimination computes an inequality description of the projection of a polyhedron onto a subset of its coordinates by eliminating one variable at a time. It is used in several areas of optimisation and computer science, and it is a standard way of obtaining the entropic constraints of a causal structure, where the marginalisation over the latent variables produces such a projection. Its limitation is the growth of the intermediate systems of inequalities, which can be doubly exponential in the number of eliminated variables even though the projection itself grows only as a single exponential. In practice the computational overload of the method therefore depends on two choices: how the redundant inequalities are removed after each step, and the order in which the variables are eliminated. We consider both. We first show, by an explicit example, that Imbert's redundancy test cannot be interleaved with redundancy removal by linear programming. We show that the two methods, however, can be combined soundly if the derivation records used by Imbert's test are re-initialised after every step at which linear programming is used. We then propose a rule for choosing the elimination order of the variables that gives a significant computational advantage, however, at the cost of increased resource usage. We demonstrate this advantage on some random polytopes, where the rule reduces the running time by factors of between 6 and 25 compared with the same elimination under a fixed order. For entropic descriptions of causal structures, with more than 250 inequalities and more than 100 variables to eliminate, our rule keeps the number of inequalities handled at each step one to two orders of magnitude lower than a fixed order.

cs.CC↗

arXiv2026

Spurious quantum correlations

In his seminal paper, Bell [Physics Physique Fizika 1, 195 (1964)] considers the correlations that result from space-like separated measurements on a pair of entangled particles. He uses relativity theory to motivate the Bell causal structure, then shows the existence of quantum correlations that cannot be explained classically within this causal structure. Classical explanations of such quantum correlations are possible in alternative causal structures, for instance, those that allow superluminal causal influences, but, as shown in [New Journal of Physics 17 033002 (2015)], all such alternative explanations require fine tuning (causation without correlation). Here we discuss the existence of spurious quantum correlations --- correlations that look quantum in one causal structure, but have a natural classical explanation in another. More precisely, there are causal structures that admit non-classical quantum correlations, but for which the same correlations have a classical explanation in another causal structure without fine tuning. The realisation in the other causal structure can also be achieved without breaking any natural constraints on the causal structure that follow from relativity theory. However, similarly to non-classical quantum correlations in the Bell causal structure, we find other causal structures with non-classical quantum correlations that do not have a classical causal explanation in any alternative causal structure without fine tuning.

quant-ph↗

arXiv2025

Closing the problem of which causal structures of up to six total nodes have a classical-quantum gap

The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally proven in a simple bipartite causal structure, but analogous results have also been shown in further causal structures. Here we study the only causal structure with six or fewer nodes in which the question of whether or not there exist quantum correlations that cannot be achieved classically was open. In this causal structure we show that such quantum correlations exist using a method that involves imposing additional restrictions on the correlations. This hence completes the picture of which causal structures of up to six nodes support non-classical quantum correlations. We also provide further illustrations of our method using other causal structures.

quant-ph↗

arXiv2024

Comment on a no-go theorem for $\psi$-ontic models

In a recent paper [Carcassi, Oldofredi and Aidala, Found Phys 54, 14 (2024)] it is claimed that the whole Harrigan--Spekkens framework of ontological models is inconsistent with quantum theory. They show this by showing that all pure quantum states in $\psi$-ontic models must be orthogonal. In this note, we identify some crucial mistakes in their argument to the extent that the main claim is incorrect.

quant-ph↗

arXiv2023

Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal structure's implied inequality constraints is generally far more difficult than enumerating its equalities. Furthermore, only inequality constraints ever admit violation by quantum correlations. For both those reasons, it is important to classify causal scenarios into those which impose inequality constraints versus those which do not. Here we develop methods for detecting such scenarios by appealing to d-separation, e-separation, and incompatible supports. Many (perhaps all?) scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey (HLP). Considering all scenarios with up to 4 observed variables, which number in the thousands, we are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.

quant-ph↗

arXiv2020

Quantum entanglement percolation under a realistic restriction

The problem of establishing Bell and Greenberger-Horne-Zeilinger states between faraway places or distant nodes of a circuit is a difficult and an extremely important one, and a strategy which addresses it is entanglement percolation. We provide a method for attaining the end through a quantum measurement strategy involving three-, two-, and single-qubit measurements on a single-layer honeycomb lattice of partially entangled pure bipartite entangled states. We then move over to a double-layered lattice, and introduce entanglement percolation on that lattice under a realistic restriction on local quantum operations and classical communication allowed on the nodes of the lattice. When applied to a single-layered honeycomb lattice, our strategy would call for less noise effects in an actual realization than when the same phenomenon is attained via existing methods. Moreover, for the double-layered honeycomb lattice, we report advantage of quantum entanglement percolation over classical entanglement percolation under the realistic restriction.

quant-ph↗