All reports by Author Rahul Jain:

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TR21-078
| 8th June 2021
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Rahul Jain, Srijita Kundu#### A direct product theorem for quantum communication complexity with applications to device-independent QKD

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TR20-131
| 20th August 2020
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Rahul Jain, Srijita Kundu#### A Direct Product Theorem for One-Way Quantum Communication

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TR17-123
| 2nd August 2017
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Dmitry Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs#### Quadratically Tight Relations for Randomized Query Complexity

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TR17-107
| 1st June 2017
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Anurag Anshu, Dmitry Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal#### A Composition Theorem for Randomized Query complexity

Revisions: 1

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TR17-054
| 22nd March 2017
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Anurag Anshu, Naresh Goud, Rahul Jain, Srijita Kundu, Priyanka Mukhopadhyay#### Lifting randomized query complexity to randomized communication complexity

Revisions: 4

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TR16-070
| 24th April 2016
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Mika Göös, Rahul Jain, Thomas Watson#### Extension Complexity of Independent Set Polytopes

Revisions: 1

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TR15-199
| 7th December 2015
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Prahladh Harsha, Rahul Jain, Jaikumar Radhakrishnan#### Relaxed partition bound is quadratically tight for product distributions

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TR15-028
| 27th February 2015
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Lila Fontes, Rahul Jain, Iordanis Kerenidis, Sophie Laplante, Mathieu Laurière, Jérémie Roland#### Relative Discrepancy does not separate Information and Communication Complexity

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TR13-158
| 18th November 2013
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Gábor Braun, Rahul Jain, Troy Lee, Sebastian Pokutta#### Information-theoretic approximations of the nonnegative rank

Revisions: 3

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TR11-033
| 8th March 2011
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Rahul Jain, Shengyu Zhang#### The influence lower bound via query elimination

Rahul Jain, Srijita Kundu

We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an $l$-player predicate $V$. In particular we show that for a distribution $p$ that is product across the input sets of the $l$ players, the success probability of any entanglement-assisted quantum communication protocol for computing $n$ ... more >>>

Rahul Jain, Srijita Kundu

We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we show that

\[ \mathrm{Q}^1_{1-(1-\varepsilon)^{\Omega(\zeta^6k/\log|\mathcal{Z}|)}}(f^k) = \Omega\left(k\left(\zeta^5\cdot\mathrm{Q}^1_{\varepsilon + 12\zeta}(f) - \log\log(1/\zeta)\right)\right),\]

where $\mathrm{Q}^1_{\varepsilon}(f)$ represents the one-way entanglement-assisted quantum communication complexity of $f$ with ...
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Dmitry Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs

Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In this paper we study a new complexity measure that we call expectational certificate complexity $EC(f)$, which is ... more >>>

Anurag Anshu, Dmitry Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal

Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $\R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow \{0,1\}$, $\R_{1/3}(f\circ g^n) = \Omega(\R_{4/9}(f)\cdot\R_{1/2-1/n^4}(g))$, where $f \circ g^n$ is the relation obtained by composing $f$ and $g$. ... more >>>

Anurag Anshu, Naresh Goud, Rahul Jain, Srijita Kundu, Priyanka Mukhopadhyay

We show that for any (partial) query function $f:\{0,1\}^n\rightarrow \{0,1\}$, the randomized communication complexity of $f$ composed with $\mathrm{Index}^n_m$ (with $m= \poly(n)$) is at least the randomized query complexity of $f$ times $\log n$. Here $\mathrm{Index}_m : [m] \times \{0,1\}^m \rightarrow \{0,1\}$ is defined as $\mathrm{Index}_m(x,y)= y_x$ (the $x$th bit ... more >>>

Mika Göös, Rahul Jain, Thomas Watson

We exhibit an $n$-node graph whose independent set polytope requires extended formulations of size exponential in $\Omega(n/\log n)$. Previously, no explicit examples of $n$-dimensional $0/1$-polytopes were known with extension complexity larger than exponential in $\Theta(\sqrt{n})$. Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit ... more >>>

Prahladh Harsha, Rahul Jain, Jaikumar Radhakrishnan

Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $${{CC}}^\mu_{0.49}(f) = O\left(\left(\log {{rprt}}_{1/4}(f) \cdot \log \log {{rprt}}_{1/4}(f)\right)^2\right),$$ where ${{CC}^\mu_\varepsilon(f)$ is the distributional communication complexity with error at most $\varepsilon$ under the distribution $\mu$ and ... more >>>

Lila Fontes, Rahul Jain, Iordanis Kerenidis, Sophie Laplante, Mathieu Laurière, Jérémie Roland

Does the information complexity of a function equal its communication complexity? We examine whether any currently known techniques might be used to show a separation between the two notions. Recently, Ganor et al. provided such a separation in the distributional setting for a specific input distribution ?. We show that ... more >>>

Gábor Braun, Rahul Jain, Troy Lee, Sebastian Pokutta

Common information was introduced by Wyner as a measure of dependence of two

random variables. This measure has been recently resurrected as a lower bound on the logarithm of the nonnegative rank of a nonnegative matrix. Lower bounds on nonnegative rank have important applications to several areas such

as communication ...
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Rahul Jain, Shengyu Zhang

We give a simpler proof, via query elimination, of a result due to O'Donnell, Saks, Schramm and Servedio, which shows a lower bound on the zero-error randomized query complexity of a function $f$ in terms of the maximum influence of any variable of $f$. Our lower bound also applies to ... more >>>