arXiv subjects

Sougata Bhattacharyya

Publications and source records attributed to Sougata Bhattacharyya.

6 recordsLinked to original sources

arXiv2026

Phase-sensitive framed-ribbon representation of single-qubit Pauli measurements in linear cluster states

We provide a geometric classification of single-qubit projective measurements on one-dimensional linear cluster states within a topological framework. Establishing an explicit correspondence between local measurements and surgery operations on an associated link model, we represent the cluster state as a linear Hopf chain. Computational-basis (Z) measurements act as topological severance for bulk qubits and boundary pruning for end qubits. Transverse-basis (X) measurements remove the measured qubit and stratify the remaining state into a superposition of two disjoint but classically correlated segments. In contrast, lateral-basis (Y) measurements preserve a single continuous spliced chain while generating complex phase factors absent from unframed link descriptions. Although the unframed linking structure already distinguishes X- and Y-basis measurement outcomes geometrically, it cannot differentiate the two possible outcomes within a fixed basis. To resolve this ambiguity, we introduce a framed ribbon representation in which quantum phases are encoded as geometric twists, with chiral plus/minus 90 deg twists representing the phases plus/minus i. The resulting framework provides a phase-sensitive, outcome-resolved geometric description of single-shot Pauli measurements on linear cluster states. The twist angles are geometric labels determined by measurement outcomes and associated by-product operators rather than topological invariants, whereas the underlying linking pattern remains a genuine topological datum. The analysis is restricted to single-shot single-qubit Pauli measurements on one-dimensional cluster states; sequential measurements and classical feedforward are left as open problems.

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arXiv2026

Geometry versus excitation sector in the decoherence of asymmetric $N$-qubit $W$ states

We investigate how network geometry and excitation sector separately control pairwise entanglement decay in asymmetric multipartite $W$ states. To disentangle these effects, we introduce an analytically tractable $N$-qubit generalization of the asymmetric Lohmayer geometry and its complementary-excitation partner, yielding inequivalent vertex-base (VB) and base-base (BB) pair classes that can be compared directly with symmetric $W$-state references. We derive closed-form concurrence dynamics under representative one-sided noise models and find that, within either excitation sector, the VB concurrence has exactly the same noise dependence as the corresponding symmetric reference, preserving a noise-independent proportional advantage wherever both remain entangled. The amplitude-damping reordering previously identified for the three-qubit Lohmayer state is therefore a cross-sector effect rather than an intrinsic fragility of the VB geometry. In contrast, the BB pair exhibits a genuine same-sector structural fragility, with lower entanglement-sudden-death thresholds than the VB pair under depolarizing noise and, in the $(N-1)$-excitation sector, under amplitude damping. The results establish network geometry, excitation sector, and noise symmetry as distinct ingredients governing pairwise entanglement robustness in asymmetric quantum networks.

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arXiv2026

Knot your average qutrit: Measurement-induced entanglement splitting and the cabling dictionary for GHZ and W States

Multipartite entanglement is conventionally classified by state families viz. family of GHZ and W class of states, with each family expected to behave differently under measurement. We show that, at least for the question of how entanglement splits after a single-particle measurement, this is not the division that matters for qutrits. Extending the Aravind's correspondence (which models entanglement as topological linking, and projective measurement as physically cutting a ring from an interlinked configuration\cite{aravind1997}) from qubits to qutrits, we derive the complete measurement-induced entanglement splitting of the GHZ type qutrit state i.e |GHZ_3> and of the full family of symmetric W class qutrit states, six two same - one different states i.e |{W_{p,p,q}^{sym}}> and one all - different state i.e. |W_{0,1,2}>, under both the computational basis (CB) and the mutually unbiased bases (MUBs), obtaining exact eigenvalues and Schmidt ranks for every outcome in every case. We see that the |W_{0,1,2}> state behaves similarly as |GHZ_3> state, a single, outcome-independent residual rank in each basis, while the |{W_{p,p,q}^{sym}> states alone show probability-weighted, outcome-dependent behaviour. The relevant structural line is therefore repeated-index versus all-different-index bag structure, not GHZ class versus $W$ class. We express this classification using a \textit{two-strand cabling} extension of Aravind's \textit{ring-and-link} picture. This is needed because the qutrit residual Schmidt rank (R) takes three values, R belonging to {1,2,3}, rather than the qubit binary (i.e. R belonging to {1,2}). We are explicit throughout that this cabling dictionary is a labeling convention built to reproduce an independently computed Schmidt rank, not a topological invariant derived from the link diagrams themselves, and we discuss what would be needed to close that gap

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arXiv2026

Super-Link Fragility in Asymmetric W-Class States under Quantum Noise

The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is $C_{VB} > C_W > C_{BB}$. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $γ$. We term this reordering as the \textit{Super-Link Fragility Effect}. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.

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arXiv2026

Entanglement, Coherence, and Recursive Linking in Dicke states : A Topological Perspective

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states $|D_n^{(k)}\rangle$. By viewing qubits as topological loops, we establish a direct correspondence between the recursive measurement dynamics of Dicke states and the stability of $n$-Hopf links. We utilize the Schmidt rank to quantify bipartite entanglement resilience and introduce the $l_1$-norm of quantum coherence as a measure of link fluidity. We demonstrate that unlike fragile states such as $ \left| GHZ \right \rangle$ (analogous to Borromean rings), Dicke states exhibit a robust, self-similar topology where local measurements preserve the global linking structure through non-vanishing residual coherence.

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arXiv2025

Symmetric and asymmetric tripartite states under the lens of entanglement splitting and topological linking

This work establishes a direct operational connection between the entanglement structures of specific three-qubit states (i.e. multipartite entanglement) and their corresponding topological links. We investigate the symmetric $\wwbar$ state and the asymmetric $\starstate$ state through local projective measurements on individual qubits. The post measurement states are analyzed via their Schmidt rank to characterize residual bipartite entanglement. For the symmetric $\wwbar$ state, measurement of any qubit consistently results in a non-maximally entangled post-measurement state (Schmidt rank 2), analogous to the behavior of a \textit{3-Hopf link} structure, where cutting any ring leaves the remaining two nontrivially linked. On the other hand, the $\starstate$ state exhibits a context-dependent fragility. Its behavior predominantly mirrors that of a \textit{3-link chain}, where severing the central qubit decouples the system, while cutting an outer qubit often preserves a residual link. Crucially, for specific measurement outcomes, the $\starstate$ state also exhibits the defining property of the \textit{Borromean rings}, where the loss of one qubit completely disentangles the remaining two. This analysis provides a concrete interpretation of topological linking structures as a resource for characterizing distributed entanglement and its resilience under local measurement operations, revealing that a single quantum state can contextually embody multiple distinct topological analogues.

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