arXiv subjects

Ashutosh Rai

Publications and source records attributed to Ashutosh Rai.

At least 37 records · Page 2Linked to original sources

arXiv2018

A Polynomial Kernel for Diamond-Free Editing

An $H$-free editing problem asks whether we can edit at most $k$ edges to make a graph contain no induced copy of the fixed graph $H$. We obtain a polynomial kernel for this problem when $H$ is a diamond. The incompressibility dichotomy for $H$ being a 3-connected graph and the classical complexity dichotomy suggest that except for $H$ being a complete/empty graph, $H$-free editing problems admit polynomial kernels only for a few small graphs $H$. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of $H$-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.

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arXiv2017

Strong Quantum Solutions in Conflicting Interest Bayesian Games

Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically-correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where average payoff of both the players exceed respective individual maximum for each player over all classically-correlated equilibriums.

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arXiv2017

Strong supremacy of quantum systems as communication resource

We investigate the task of $d$-level random access codes ($d$-RACs) and consider the possibility of encoding classical strings of $d$-level symbols (dits) into a quantum system of dimension $d'$ strictly less than $d$. We show that the average success probability of recovering one (randomly chosen) dit from the encoded string can be larger than that obtained in the best classical protocol for the task. Our result is intriguing as we know from Holevo's theorem (and more recently from Frenkel-Weiner's result [Commun. Math. Phys. 340, 563 (2015)]) that there exist communication scenarios wherein quantum resources prove to be of no advantage over classical resources. A distinguishing feature of our protocol is that it establishes a stronger quantum advantage in contrast to the existing quantum $d$-RACs where $d$-level quantum systems are shown to be advantageous over their classical $d$-level counterparts.

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arXiv2016

Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities

One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parity-oblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such tasks in any preparation noncontextual theory. These bounds constitute noncontextuality inequalities for any value of d. For d=3, using a set of mutually asymmetric biased bases we show that the corresponding noncontextual bound is violated by quantum theory. We also show quantum violation of the inequalities for some other higher values of d. This reveals operational usefulness of preparation contextuality of higher level quantum systems.

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arXiv2015

A Parameterized Algorithm for Mixed Cut

The classical Menger's theorem states that in any undirected (or directed) graph $G$, given a pair of vertices $s$ and $t$, the maximum number of vertex (edge) disjoint paths is equal to the minimum number of vertices (edges) needed to disconnect from $s$ and $t$. This min-max result can be turned into a polynomial time algorithm to find the maximum number of vertex (edge) disjoint paths as well as the minimum number of vertices (edges) needed to disconnect $s$ from $t$. In this paper we study a mixed version of this problem, called Mixed-Cut, where we are given an undirected graph $G$, vertices $s$ and $t$, positive integers $k$ and $l$ and the objective is to test whether there exist a $k$ sized vertex set $S \subseteq V(G)$ and an $l$ sized edge set $F \subseteq E(G)$ such that deletion of $S$ and $F$ from $G$ disconnects from $s$ and $t$. We start with a small observation that this problem is NP-complete and then study this problem, in fact a much stronger generalization of this, in the realm of parameterized complexity. In particular we study the Mixed-Multiway Cut-Uncut problem where along with a set of terminals $T$, we are also given an equivalence relation $\mathcal{R}$ on $T$, and the question is whether we can delete at most $k$ vertices and at most $l$ edges such that connectivity of the terminals in the resulting graph respects $\mathcal{R}$. Our main results is a fixed parameter algorithm for Mixed-Multiway Cut-Uncut using the method of recursive understanding introduced by Chitnis et al. (FOCS 2012).

cs.DS↗

arXiv2015

Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound

Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given operational theory, the maximum success probability achievable in such a game suffices as a \emph{bona-fide} measure of preparation contextuality for the underlying theory. In this work we show that preparation contextuality in quantum theory is more restricted compared to a general operational theory known as \emph{box world}. Moreover, we find that this limitation of quantum theory implies the quantitative bound on quantum nonlocality as depicted by the Cirel'son bound.

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arXiv2013

Local Orthogonality provides better upper bound for Hardy's nonlocality

The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics---viz. explaining the Cirel'son bound. However, these principles are not that much successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that, a newly proposed physical principle namely Local Orthogonality does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.

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arXiv2013

Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound

Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH scenario, ML along with constraint of equal-biasness for the concerned observables, almost reproduces the quantum joint probability distribution corresponding to maximal quantum Bell violation, which is unique up to relabeling. From this example and earlier work of Cavalcanti, Salles and Scarani, we conclude that IC and ML are in-equivalent physical principles; satisfying one does not imply that the other is satisfied.

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arXiv2013

Polynomial Kernels for λ-extendible Properties Parameterized Above the Poljak-Turzík Bound

Poljak and Turzik (Discrete Mathematics 1986) introduced the notion of λ-extendible properties of graphs as a generalization of the property of being bipartite. They showed that for any 0 < λ < 1 and λ-extendible property Π, any connected graph G on n vertices and m edges contains a spanning subgraph H in Π with at least λm + (1-λ)(n-1)/2 edges. The property of being bipartite is λ-extendible for λ = 1/2, and so the Poljak-Turzik bound generalizes the well-known Edwards-Erdos bound for Max-Cut. Other examples of λ-extendible properties include: being an acyclic oriented graph, a balanced signed graph, or a q-colorable graph for some integer q. Mnich et. al. (FSTTCS 2012) defined the closely related notion of strong λ-extendibility. They showed that the problem of finding a subgraph satisfying a given strongly λ-extendible property Π is fixed-parameter tractable (FPT) when parameterized above the Poljak-Turzik bound - does there exist a spanning subgraph H of a connected graph G such that H in Π and H has at least λm + (1-λ)(n-1)/2 + k edges? - subject to the condition that the problem is FPT on a certain simple class of graphs called almost-forests of cliques. In this paper we settle the kernelization complexity of nearly all problems parameterized above Poljak-Turzik bounds, in the affirmative. We show that these problems admit quadratic kernels (cubic when λ = 1/2), without using the assumption that the problem is FPT on almost-forests of cliques. Thus our results not only remove the technical condition of being FPT on almost-forests of cliques from previous results, but also unify and extend previously known kernelization results in this direction. Our results add to the select list of generic kernelization results known in the literature.

cs.DM↗

arXiv2013

A testable prediction of the no-signalling condition using a variant of the EPR-Bohm example

Predictive power of the no-signalling condition (NSC) is demonstrated in a testable situation involving a non-ideal Stern-Gerlach (SG) device in one of the two wings of the EPR-Bohm entangled pairs. In this wing, for two types of measurement in the other wing, we consider the spin state of a selected set of particles that are confined to a particular half of the plane while emerging from the SG magnetic field region. Due to non-idealness of the SG setup, this spin state will have superposing components involving a relative phase for which a testable quantitative constraint is obtained by invoking NSC, thereby providing a means for precision testing of this fundamentally significant principle.

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arXiv2012

Maximum tri-partite Hardy's nonlocality respecting all bi-partite principles

The set of multiparty correlations that respect all bi-partite principles has been conjectured to be same as the set of time-ordered-bi-local correlations. Based on this conjuncture we find the maximum value of success probability of tri-partite Hardy's correlation respecting all bi-partite physical principles. Unlike in quantum mechanics, the no-signaling principle does not reveal any gap in Hardy's maximum success probability for bi-partite and tri-partite system. Information causality principle is shown to be successful in qualitatively revealing this quantum feature and this result is independent of the conjecture mentioned above.

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arXiv2012

Local simulation of singlet statistics for restricted set of measurement

The essence of Bell's theorem is that, in general, quantum statistics cannot be reproduced by local hidden variable (LHV) model. This impossibility is strongly manifested while analyzing the singlet state statistics for Bell-CHSH violations. In this work, we provide various subsets of two outcome POVMs for which a local hidden variable model can be constructed for singlet state.

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arXiv2012

Hardy's nonlocality argument as witness for post-quantum correlation

Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish similar result by using device independent success probability of Hardy's nonlocality argument for tripartite quantum system. We construct an example of a tri-partite Hardy correlation which is post-quantum but satisfies not only all bipartite information principle but also the GYNI inequality.

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arXiv2012

Optimal free-will on one side in reproducing the singlet correlation

Bell's theorem teaches us that there are quantum correlations that can not be simulated by just shared randomness (Local Hidden variable). There are some recent results which simulate singlet correlation by using either 1 cbit or a binary (no-signaling) correlation which violate Bell's inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, MJW Hall showed that the statistics of singlet state can be generated by sacrificing measurement independence where underlying distribution of hidden variables depend on measurement direction of both parties [Phys. Rev. Lett.105 250404 (2010)]. He also proved that for any model of singlet correlation, 86% measurement independence is optimal. In this paper, we show that 59% measurement independence is optimal for simulating singlet correlation when the underlying distribution of hidden variables depend only on measurements of one party. We also show that a distribution corresponding to this optimal lack of free will, already exists in literature which first appeared in the context of detection efficiency loophole.

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arXiv2011

Leggett-type nonlocal realist inequalities without any constraint on the geometrical alignment of measurement settings

Leggett-type nonlocal realist inequalities that have been derived to date are all contingent upon suitable geometrical constraints to be strictly satisfied by the spatial arrangement of the relevant measurement settings. This undesirable restriction is removed in the present work by deriving appropriate forms of nonlocal realist inequalities, one of which involve the least number of settings compared to all such inequalities derived earlier. The way such inequalities would provide a logically firmer basis for a clearer testing of Leggett-type nonlocal realist model vis-a-vis quantum mechanics is explained.

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arXiv2011

A complementary relation between classical bits and randomness in local part in simulating singlet state

Recently Leggett's proposal of non-local model generates new interest in simulating the statistics of singlet state. Singlet state statistics can be simulated by 1 bit of classical communication without using any further nonlocal correlation. But, interestingly, singlet state statistics can also be simulated with no classical cost if a non-local box is used. In the first case, the output is completely unbiased whereas in second case outputs are completely random. We suggest a new (possibly) signaling correlation resource which successfully simulates singlet statistics and this result suggests a new complementary relation between required classical bits and randomness in local output when the classical communication is limited by 1 cbit. This result reproduces the above two models of simulation as extreme cases. This also explains why Leggett's non-local model and the model presented by Branciard et.al. should fail to reproduce the statistics of a singlet.

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arXiv2010

Local randomness in Hardy's correlations: Implications from information causality principle

Study of nonlocal correlations in term of Hardy's argument has been quite popular in quantum mechanics. Recently Hardy's argument of non-locality has been studied in the context of generalized non-signaling theory as well as theory respecting information causality. Information causality condition significantly reduces the success probability for Hardy's argument when compared to the result based on non-signaling condition. Here motivated by the fact that maximally entangled state in quantum mechanics does not exhibit Hardy's non-local correlation, we do a qualitative study of the property of local randomness of measured observable on each side reproducing Hardy's non-locality correlation,in the context of information causality condition. On applying the necessary condition for respecting the principle of information causality, we find that there are severe restrictions on the local randomness of measured observable in contrast to results obtained from no-signaling condition.Still, there are some restrictions imposed by quantum mechanics that are not obtained from information causality condition.

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arXiv2010

Bound on Hardy's non-locality from the principle of Information Causality

Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but still much less than what the nosignaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy's argument) in this context.

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