arXiv subjects

Anushko Chattopadhyay

Publications and source records attributed to Anushko Chattopadhyay.

3 recordsLinked to original sources

arXiv2026

Emergence and Recovery of (logical) Kochen-Specker Contextuality via Hamilton Extension

Logical Kochen-Specker (KS) contextuality is widely regarded as an intrinsic property of specially constructed measurement configurations. We show instead that it can emerge from KS-colorable vector sets through a constructive procedure we call the Hamilton extension. Defined for four-dimensional vector sets, the Hamilton extension associates each real vector with a measurement context while inducing additional measurement contexts among Hamilton-extended children of distinct parent vectors. These emergent contexts fundamentally alter the compatibility structure, transforming KS-colorable configurations into KS-uncolorable ones and recovering logical contextuality lost under apex-vertex augmentation. We establish a sharp and optimal threshold -- the Hamilton extension of every five-vector parent set remains KS-colorable, whereas suitably chosen six-vector parent sets already generate logical KS contradictions. Thus, six vectors constitute the smallest parent set capable of generating KS contradiction through this mechanism. Our results reveal a new structural route to contextuality, provide a systematic framework for constructing compact KS sets, and have implications for contextuality-based quantum information protocols and graph-theoretic approaches to nonclassicality.

quant-ph↗

arXiv2026

Conclusive Identification Via Noisy Classical Channel: Superactivation and Quantum Advantage

We introduce conclusive identification task for classical channels: a receiver identifies transmitted inputs without error when possible, and responds inconclusively when outputs are ambiguous. For a symmetric not-fully-corrupted channel $N : X \to X$, the single-shot conclusive identification index $\mathrm{ci}_\circ(N)$ counts the maximum number of conclusively identifiable inputs. We show $\mathrm{ci}_\circ(N)$ exhibits a striking superactivation phenomenon: a channel with $\mathrm{ci}_\circ(N) = 0$ achieves $\mathrm{ci}_\circ(N \otimes \mathrm{id}^c_β) = |X|$ when assisted by a perfect classical channel of dimension $β< |X|$. The minimum classical assistance required equals the chromatic number $χ(\mathtt{S}_N)$ of the channel's support graph $\mathtt{S}_N$. We provide channel families where the superactivation gap $\mathrm{ci}_\circ(N \otimes \mathrm{id}^c_β) - \mathrm{ci}_\circ(\mathrm{id}^c_β)$ can be made arbitrarily large. A noiseless quantum channel of dimension equal to the orthogonal rank $ξ(\mathtt{S}_N)$ suffices, yielding a strict quantum advantage whenever $ξ(\mathtt{S}_N) < χ(\mathtt{S}_N)$. This advantage is demonstrated through three explicit constructions motivated by combinatorial and algebraic state-independent, and state-dependent proofs of Kochen-Specker contextuality. Via the co-normal product of graphs, we analyze the scaling of the quantum advantage ratio $χ_f(\mathtt{S}_N)/ξ(\mathtt{S}_N)$, and present a channel for which quantum assistance is exponentially more efficient than classical. Our results establish $\mathtt{S}_N$, rather than the confusability graph $\mathtt{G}_N$, as the natural combinatorial object for conclusive identification, revealing that channels deemed useless under Shannon's zero-error framework can exhibit rich superactivation and quantum advantage, with deep connections to quantum contextuality.

quant-ph↗

arXiv2026

Superadditivity of Zero-Error Capacity in Noisy Classical and Perfect Quantum Channel Pairs

We demonstrate superadditivity of one-shot zero-error classical capacity in an asymmetric communication setting where a noisy classical channel is used in parallel with a perfect quantum channel. Each channel individually supports only a fixed number of perfectly distinguishable messages. Their joint use enables transmission of strictly more messages than permitted by the product of the individual capacities. We present explicit constructions achieving this enhancement and establish that replacing the perfect quantum channel with a perfect classical channel eliminates the effect. Finally, we identify a structural criterion on the noisy channel governing this effect and show that the quantum advantage is rooted in Kochen-Specker contextuality.

quant-ph↗