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Sk Sazim

Publications and source records attributed to Sk Sazim.

At least 19 recordsLinked to original sources
arXiv2024

Multiple-shot labeling of quantum observables

Quantum labeling tasks ask one to recover the missing associations between classical outcome labels and the effects forming the POVM. We study labeling in the multiple-shot regime, allowing a finite number of uses of the device and the most general tester-based strategies, including adaptivity. For binary observables, we show that if perfect labeling is impossible in a single shot, then it remains impossible with any finite number of shots. In particular, we derive the formula for minimum-error performance and highlight its ``even-odd" behavior. For non-binary observables, we derive the optimal single-shot minimum-error success probability in closed form, and show that entanglement assistance does not improve this optimum. We also provide finite-shot schemes for (perfect or partial) labeling and give illustrative examples, including the qubit trine POVM where the optimal two-shot success probability is computed explicitly.

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arXiv2024

Higher-order incompatibility improves distinguishability of causal quantum networks

Higher-order quantum theory deals with causal quantum processes, described by quantum combs, and test procedures, described by quantum testers, "measuring" these processes. In this work, we show that "jointly non-implementable" or incompatible quantum testers perform better in distinguishability tasks than their compatible counterparts. To demonstrate our finding, we consider a specific two-party game based on distinguishing quantum combs. We show that the player does better at winning the game when they have exclusive access to incompatible testers over compatible ones. Moreover, we show that, using the resource theoretic measure convex weight, any general quantum resource present in testers is resourceful in quantum comb exclusion tasks. These investigations generalise, respectively, an earlier finding that incompatibility of quantum observables to be a bona fide resource in quantum state distinguishability tasks and another finding that any resource present in observables result in improved performance in state exclusion or antidistinguishability tasks.

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arXiv2024

Certification of multi-qubit quantum systems with temporal inequalities

Demonstrating contextual correlations in quantum theory through the violation of a non-contextuality inequality necessarily needs some ``contexts" and thus assumes some compatibility relations between the measurements. As a result, any self-testing protocol based on the maximal violation of such inequality is not free from such assumptions. In this work, we propose temporal inequalities derived from non-contextuality inequalities for multi-qubit systems without assuming any compatibility relations among the measurements. We demonstrate that the new inequalities can be maximally violated via a sequential measurement scenario. Moreover, using the maximal violation of these temporal inequalities we are able to certify multi-qubit graph states and the measurements.

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arXiv2024

Bloch sphere analog of qudits using Heisenberg-Weyl Operators

We study an analogous Bloch sphere representation of higher-level quantum systems using the Heisenberg-Weyl operator basis. We introduce a parametrization method that will allow us to identify a real-valued Bloch vector for an arbitrary density operator. Before going into arbitrary $d$-level ($d\geq 3$) quantum systems (qudits), we start our analysis with three-level ones (qutrits). It is well known that we need at least eight real parameters in the Bloch vector to describe arbitrary three-level quantum systems (qutrits). However, using our method we can divide these parameters into four weight, and four angular parameters, and find that the weight parameters are inducing a unit sphere in four-dimension. And, the four angular parameters determine whether a Bloch vector is physical. Therefore, unlike its qubit counterpart, the qutrit Bloch sphere does not exhibit a solid structure. Importantly, this construction allows us to define different properties of qutrits in terms of Bloch vector components. We also examine the two and three-dimensional sections of the sphere, which reveal a non-convex yet closed structure for physical qutrit states. Further, we apply our representation to derive mutually unbiased bases (MUBs), characterize unital maps for qutrits, and assess ensembles using the Hilbert-Schmidt and Bures metrics. Moreover, we extend this construction to qudits, showcasing its potential applicability beyond the qutrit scenario.

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arXiv2024

Trade-off between Bagging and Boosting for quantum separability-entanglement classification

Certifying whether an arbitrary quantum system is entangled or not, is, in general, an NP-hard problem. Though various necessary and sufficient conditions have already been explored in this regard for lower dimensional systems, it is hard to extend them to higher dimensions. Recently, an ensemble bagging and convex hull approximation (CHA) approach (together, BCHA) was proposed and it strongly suggests employing a machine learning technique for the separability-entanglement classification problem. However, BCHA does only incorporate the balanced dataset for classification tasks which results in lower average accuracy. In order to solve the data imbalance problem in the present literature, an exploration of the Boosting technique has been carried out, and a trade-off between the Boosting and Bagging-based ensemble classifier is explored for quantum separability problems. For the two-qubit and two-qutrit quantum systems, the pros and cons of the proposed random under-sampling boost CHA (RUSBCHA) for the quantum separability problem are compared with the state-of-the-art CHA and BCHA approaches. As the data is highly unbalanced, performance measures such as overall accuracy, average accuracy, F-measure, and G-mean are evaluated for a fair comparison. The outcomes suggest that RUSBCHA is an alternative to the BCHA approach. Also, for several cases, performance improvements are observed for RUSBCHA since the data is imbalanced.

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arXiv2023

Certification of two-qubit quantum systems with temporal inequality

Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Ref. [Phys. Rev. \textbf{A} 101, 032106 (2020)], a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this work, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from non-contextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.

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arXiv2022

Mermin and Svetlichny inequalities for non-projective measurement observables

The necessary and sufficient criteria for violating the Mermin and Svetlichny inequalities by arbitrary three-qubit states are presented. Several attempts have been made, earlier, to find such criteria, however, those extant criteria are neither tight for most of the instances, nor fully general. We generalize the existing criteria for Mermin and Svetlichny inequalities which are valid for the local projective measurement observables as well as for the arbitrary ones. We obtain the maximal achievable bounds of the Mermin and Svetlichny operators with unbiased measurement observables for arbitrary three-qubit states and with arbitrary observables for three-qubit states having maximally mixed marginals. We find that for certain ranges of measurement strengths, it is possible to violate Mermin and Svetlichny inequalities only by biased measurement observables. The necessary and sufficient criteria of violating any one of the six possible Mermin and Svetlichny inequalities are also derived.

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arXiv2021

Creation of quantum coherence with general measurement processes

Quantum measurement not only can destroy coherence but also can create it. Here, we estimate the maximum amount of coherence, one can create under a complete non-selective measurement process. For our analysis, we consider projective as well as POVM measurements. Based on our observations, we characterize the measurement processes into two categories, namely, the measurements with the ability to induce coherence and the ones without this ability. Our findings also suggest that the more POVM elements present in a measurement that acts on the quantum system, the less will be its coherence creating ability. We also introduce the notion of raw coherence in the POVMs that helps to create quantum coherence. Finally, we find a trade-off relation between the coherence creation, entanglement generation between system and apparatus, and the mixedness of the system in a general measurement setup.

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arXiv2021

Role of fine-grained uncertainty in determining the limit of preparation contextuality

The optimal success probability of a communication game sets fundamental limitations on an operational theory. Quantum advantage of parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102, 010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of fine-grained uncertainty relation to the success probability of PORAC game played with the quantum resource. Subsequently, we find the optimal success probability for the 2-dit PORAC game using MUBs for the decoding strategy. Finally, we also derive an upper bound on quantum advantage for the N-dit PORAC game.

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arXiv2021

Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with $N$ depolarizing channels put in superposition of $M$ causal orders via quantum SWITCH. We calculate Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with $M$ and it is independent of $N$. For a qubit it never reaches $1$ if we are increasing $M$. On the other hand, the classical capacity decreases with the dimension $d$ of the message system. Further, for $N=3$ and $N=4$ we studied superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by cyclic permutation subgroup.

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arXiv2020

Resource state structure for controlled quantum key distribution

Quantum entanglement plays a pivotal role in many communication protocols, like secret sharing and quantum cryptography. We consider a scenario where more than two parties are involved in a protocol and share a multipartite entangled state. In particular, we considered the protocol of Controlled Quantum Key Distribution (CoQKD), introduced in the Ref. Chin. Phys. Lett. 20, 183-185 (2003), where, two parties, Alice and Bob establish a key with the cooperation of other parties. Other parties control/supervise whether Alice and Bob can establish the key, its security and key rate. We discuss the case of three parties in detail and find suitable resource states. We discuss the controlling power of the third party, Charlie. We also examine the usefulness of the new resource states for generating conference key and for cooperative teleportation. We find that recently introduced Bell inequalities can be useful to establish the security of the conference key. We also generalize the scenario to more than three parties.

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arXiv2020

Robustness of interferometric complementarity under Decoherence

Interferometric complementarity is known to be one of the most nonclassical manifestations of the quantum formalism. It is commonly known as wave-particle duality and has been studied presently from the perspective of quantum information theory where wave and particle nature of a quantum system, called quanton, are characterised by coherence and path distinguishability respectively. We here consider the effect of noisy detectors on the complementarity relation. We report that by suitably choosing the initial quanton and the detector states along with the proper interactions between the quanton and the detectors, one can reduce the in uence of noisy environment on complementarity, thereby pushing it towards saturation. To demonstrate this, three kinds of noise on detectors and their roles on the saturation of the complementarity relation are extensively studied. We also observe that for fixed values of parameters involved in the process, asymmetric quanton state posses low value of coherence while it can have a higher amount of distinguishability, and hence it has the potential to enhance the duality relation.

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arXiv2019

Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.

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arXiv2019

Quantum mutual information and quantumness vectors for multi-qubit systems

We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information -- the interaction information and generalize it to multiparticle quantum systems. There are a number of different possible generalizations. We consider two of them. One of them is related to the notion of quantum discord and the other to the concept of quantum dissension. This new measure, called dissension vector, is a set of numbers -- quantumness vector. This can be thought of as a fine-grained measure, as opposed to measures that quantify some average quantum properties of a system. These quantities quantify/characterize the correlations present in multiparticle states. We consider some multiqubit states and find that these quantities are responsive to different aspects of quantumness, and correlations present in a state. We find that different dissension vectors can track the correlations (both classical and quantum), or quantumness only. As physical applications, we find that these vectors might be useful in several information processing tasks. We consider the role of dissension vectors -- (a) in deciding the security of BB84 protocol against an eavesdropper and (b) in determining the possible role of correlations in the performance of Grover search algorithm. Especially, in the Grover search algorithm, we find that dissension vectors can detect the correlations and show the maximum correlations when one expects.

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arXiv2019

Tight upper bound for the maximal expectation value of the Mermin operators

The violation of the Mermin inequality (MI) for multipartite quantum states guarantees the existence of nonlocality between either few or all parties. The detection of optimal MI violation is fundamentally important, but current methods only involve numerical optimizations, thus hard to find even for three-qubit states. In this paper, we provide a simple and elegant analytical method to achieve the upper bound of Mermin operator for arbitrary three-qubit states. Also, the necessary and sufficient conditions for the tightness of the bound for some class of tri-partite states has been stated. Finally, we suggest an extension of this result for up to n qubits.

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arXiv2018

Coherence of quantum channels

We investigate the coherence of quantum channels using the Choi-Jamiołkowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when the channel has certain purity. This duality has been depicted via the Coherence-Purity (Co-Pu) diagrams. In particular, we study the quantum coherence of the unital and non-unital qubit channels and find out the allowed region of coherence for a fixed purity. We also study coherence of different incoherent channels, namely, incoherent operation (IO), strictly incoherent operation (SIO), physical incoherent operation (PIO) etc. Interestingly, we find that the allowed region for different incoherent operations maintain the relation $PIO\subset SIO \subset IO$. In fact, we find that if PIOs are coherence preserving operations (CPO), its coherence is zero otherwise it has unit coherence and unit purity. Interestingly, different kinds of qubit channels can be distinguished using the Co-Pu diagram. The unital channels generally do not create coherence whereas some nonunital can. All coherence breaking channels are shown to have zero coherence, whereas, this is not usually true for entanglement breaking channels. It turns out that the coherence preserving qubit channels have unit coherence. Although the coherence of the Choi matrix of the incoherent channels might have finite values, its subsystem contains no coherence. This indicates that the incoherent channels can either be unital or nonunital under some conditions.

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arXiv2018

Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity

We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty as well as conditional variance and show that conditioning on more observable reduces the uncertainty. Given three observables, we prove a 'strong sub-additivity' relation for the conditional uncertainty under certain condition. As an application, we show that using the conditional variance one can detect bipartite higher dimensional entangled states. The efficacy of our detection method lies in the fact that it gives better detection criteria than most of the existing criteria based on geometry of the states. Interestingly, we find that for $N$-qubit product states, the mutual uncertainty is exactly equal to $N-\sqrt{N}$, and if it is other than this value, the state is entangled. We also show that using the mutual uncertainty between two observables, one can detect non-Gaussian steering where Reid's criteria fails to detect. Our results may open up a new direction of exploration in quantum theory and quantum information using the mutual uncertainty, conditional uncertainty and the strong sub-additivity for multiple observables.

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