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Kailash Misra

Publications and source records attributed to Kailash Misra.

9 recordsLinked to original sources
arXiv2026

Unified monogamy and polygamy relations for multipartite systems

For a bipartite entanglement measure $\mathcal{E}$ that satisfies the $\gamma$th-power monogamy inequality (Eq.~\eqref{e:chap1-ineq1}), and for its assisted counterpart $\mathcal{E}_a$ that obeys the $\delta$th-power polygamy inequality (Eq.~\eqref{e:chap1-ineq2}), we introduce a unified, tunable framework indexed by a parameter $m\geq1$. Within this framework, we derive two hierarchical families of refined inequalities: a tightened $\alpha$-power monogamy relation for $\mathcal{E}$, valid for all $\alpha \geq m\gamma$; a tightened $\beta$-power polygamy relation for $\mathcal{E}_a$, applicable for $(m-1)\delta < \beta \leq m\delta$. As $m$ increases, the bounds become progressively tighter, recovering known results at $m=1$. Notably, the optimal monogamy bound emerges as a piecewise function of $\alpha$, with additional correction terms activated as $\alpha$ crosses successive integer thresholds, thereby offering a sharper characterization of entanglement distribution. We demonstrate that our results generalize and strengthen existing monogamy and polygamy relations through analytical comparisons and numerical evaluations using concurrence and concurrence of assistance. This hierarchical, parameterized approach offers enhanced and flexible tools for applications in quantum communication, quantum networks, and multipartite quantum information processing.

quant-ph↗
arXiv2026

State-independent uncertainty relations on multipartite spin $1/2$-systems

Uncertainty relations quantify fundamental limits on simultaneous measurement of quantum observables. While conventional formulations are state-dependent, state-independent uncertainty relations (SIURs) impose universal bounds determined solely by the algebraic structure of the operators, with applications across metrology, quantum cryptography, and entanglement detection. Despite extensive study, exact analytical variance-based SIURs have so far been established primarily for one- and bi-partite systems, while entropic SIURs have been extended to multipartite and memory-assisted settings through information-theoretic constructions. In contrast, exact variance-based SIURs beyond the bipartite level have remained analytically unresolved.} Here we develop a representation-theoretic framework for multipartite SIURs in collective spin-$\tfrac{1}{2}$ systems. Using the Clebsch--Gordan decomposition and extremal analysis of total spin variance, we derive exact state-independent bounds up to quintipartite systems. A clear structural dichotomy emerges: odd $n$ systems exhibit strictly positive universal bounds (e.g., $\Delta^2(\mathfrak{su}_2)\!\ge\!4/11$ for $n=3$), whereas even $n$ admit vanishing variance on trivial sectors but retain positive reduced-space bounds (e.g., $\Delta^2(\mathfrak{su}_2)\!\ge\!1/8$ for $n=4$). These results establish the first unified, algebraic framework for multipartite variance-based SIURs in qubit ensembles.

quant-ph↗
arXiv2025

Superior monogamy and polygamy relations and estimates of concurrence

It is well known that any well-defined bipartite entanglement measure $\mathcal{E}$ obeys $\gamma$th-monogamy relations Eq. (1.1) and assisted measure $\mathcal{E}_{a}$ obeys $\delta$th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $\alpha$th $(\alpha\geq\gamma)$ power based on Eq. (1.1). This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner. In the first part of the paper, the following three basic problems are focused: (i) tighter monogamy relation for the $\alpha$th ($0\leq \alpha\leq \gamma$) power of any bipartite entanglement measure $\mathcal{E}$ based on Eq. (1.1); (ii) tighter polygamy relation for the $\beta$th ($ \beta \geq \delta$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2); (iii) tighter polygamy relation for the $\omega$th ($0\leq \omega \leq \delta$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $\omega$th ($0\leq \omega \leq 2$) power of CoA, we obtain good estimates or bounds for the $\omega$th ($0\leq \omega \leq 2$) power of concurrence for any $N$-qubit pure states $|\psi\rangle_{AB_{1}\cdots B_{N-1}}$ under the partition $AB_{1}$ and $B_{2}\cdots B_{N-1}$. Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.

quant-ph↗
arXiv2024

Tighter parameterized monogamy relations

We seek a systematic tightening method to represent the monogamy relation for some measure in multipartite quantum systems. By introducing a family of parametrized bounds, we obtain tighter lowering bounds for the monogamy relation compared with the most recently discovered relations. We provide detailed examples to illustrate why our bounds are better.

quant-ph↗
arXiv2015

Imaginary Verma Modules for $U_q(\widehat{\mathfrak{sl}(2)})$ and Crystal-like bases

We consider imaginary Verma modules for quantum affine algebraU_q(\widehat{\mathfrak{sl}(2)}) and define a crystal-like base which we call an imaginary crystal basis using the Kashiwara algebra K_q constructed in earlier work of the authors. In particular, we prove the existence of imaginary like bases for a suitable category of reduced imaginary Verma modules for U_q(\widehat{\mathfrak{sl}(2)}).

math.RT↗
arXiv2009

Bosonic realization of toroidal Lie algebras of classical types

Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to construct toroidal Lie algebras of types $A_n, B_n$, $C_n$ and $D_n$ of level $-1, -2, -1/2$ and -2 respectively. In particular, our construction also gives new bosonic construction for the orthogonal Lie algebras in the cases of affine Lie algebras.

math.QA↗
arXiv2000

On Multi-color partitions and the generalized Rogers-Ramanujan identities

Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers-Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is representation theory of infinite dimensional Lie algebras, where various known interpretations of these identities have led to interesting applications. Motivated by their connections with Lie algebra representation theory, we give a new interpretation of a sum related to generalized Rogers-Ramanujan identities in terms of multi-color partitions.

math.CO↗