arXiv subjects

Palash Pandya

Publications and source records attributed to Palash Pandya.

7 recordsLinked to original sources

arXiv2026

Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest $(2,2,2)$ scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the $(2,2,3)$ scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.

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arXiv2023

Minimum Hilbert-Schmidt distance for Schmidt rank 2 states

The Hilbert-Schmidt distance between two states is proven to be non-contractive under CPTP maps, and therefore is not considered as an entanglement measure. However, that alone does not imply that the minimum Hilbert-Schmidt distance from the set of separable states is not contractive as well. To the contrary, not only do we provide a closed-form expression, we also provide analytical and numerical proof that minimum Hilbert-Schmidt distance for a given bipartite quantum state of Schmidt rank 2 is non-increasing under LOCC. The minimisation is taken to be over the set of separable states. We apply the algorithm by Verstraete et al [Journal of Modern Optics, 49(8), 2002] for the derivation of the analytical expression and Nielsen's theorem for the proof of monotonicity of the distance under LOCC.

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arXiv2022

An elegant proof of self-testing for multipartite Bell inequalities

The predictions of quantum theory are incompatible with local-causal explanations. This phenomenon is called Bell non-locality and is witnessed by violation of Bell-inequalities. The maximal violation of certain Bell-inequalities can only be attained in an essentially unique manner. This feature is referred to as self-testing and constitutes the most accurate form of certification of quantum devices. While self-testing in bipartite Bell scenarios has been thoroughly studied, self-testing in the more complex multipartite Bell scenarios remains largely unexplored. This work presents a simple and broadly applicable self-testing argument for N-partite correlation Bell inequalities with two binary outcome observables per party. Our proof technique forms a generalization of the Mayer-Yao formulation and is not restricted to linear Bell-inequalities, unlike the usual sum of squares method. To showcase the versatility of our proof technique, we obtain self-testing statements for N party Mermin-Ardehali-Belinskii-Klyshko (MABK) and Werner-Wolf-Weinfurter-\.Zukowski-Brukner (WWW\.ZB) family of linear Bell inequalities, and Uffink's family of N party quadratic Bell-inequalities.

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arXiv2020

Hilbert-Schmidt distance and entanglement witnessing

Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert Schmidt Distance does not form a proper entanglement measure, it can nevertheless be useful for witnessing entanglement. We provide here a few methods based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outputs successively improved approximations to the Closest Separable State for the given state. We demonstrate the efficacy of the method with examples.

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arXiv2020

Distance between Bound Entangled States from Unextendible Product Bases and Separable States

We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendibleproduct basis bound entangled states (UPB BE states). The method relies on the fact that an optimalentanglement witness is given by a plane perpendicular to a line between the reference state, entanglementof which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds anapproximation of CSS. In this article, we investigate if this approximation can be good enough toyield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those givenby Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us to learnabout the amount of entanglement and we find a relationship between it and a feature of the constructionof UPB BE states, namely the size of their central tile. We show that in most studied cases, witnessesfound with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections ina realization of the state.

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arXiv2018

Subadditivity of logarithm of violation of geometric Bell inequalities for qudits

Geometrical Bell Inequalities (GBIs) are the strongest known Bell inequalities for collections of qubits. However, their generalizations to other systems is not yet fully understood. We formulate GBIs for an arbitrary number $N$ of observers, each of which possesses a particle of an arbitrary dimension $d$. The whole $(d-1)$-parameter family of local observables with eigenbases unbiased to the computational basis is used, but it is immediate to use a discrete subset of them. We argue analytically for qutrits and numerically for other systems that the violations grows exponenetially with $N$. Within the studied range, the violation also grows with $d$. Interestingly, we observe that the logarithm of the violation ratio for ququats grows with $N$ slower than the doubled logarithm of the violation ratio for qubits, which implies a kind of subadditivity.

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arXiv2016

Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States

We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the reduced bipartite systems of the three qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information theoretic paradigm. The aforementioned complementary relation has also been established for three qubit pure states for the generalized geometric measure and the discord monogamy score respectively. The complementarity between the Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell inequality violation in the reduced two qubit system comes at the cost of the total tripartite correlation present in the entire system.

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