arXiv subjects

Anirban Pathak

Publications and source records attributed to Anirban Pathak.

At least 109 records · Page 6Linked to original sources

arXiv2017

Quantum Conference

A notion of quantum conference is introduced in analogy with the usual notion of a conference that happens frequently in today's world. Quantum conference is defined as a multiparty secure communication task that allows each party to communicate their messages simultaneously to all other parties in a secure manner using quantum resources. Two efficient and secure protocols for quantum conference have been proposed. The security and efficiency of the proposed protocols have been analyzed critically. It is shown that the proposed protocols can be realized using a large number of entangled states and group of operators. Further, it is shown that the proposed schemes can be easily reduced to protocol for multiparty quantum key distribution and some earlier proposed schemes of quantum conference, where the notion of quantum conference was different.

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arXiv2016

Quantum sealed-bid auction using a modified scheme for multiparty circular quantum key agreement

A feasible, secure and collusion-attack-free quantum sealed-bid auction protocol is proposed using a modified scheme for multi-party circular quantum key agreement. In the proposed protocol, the set of all ($n$) bidders is grouped in to $l$ subsets (sub-circles) in such a way that only the initiator (who prepares the quantum state to be distributed for a particular round of communication and acts as the receiver in that round) is a member of all the subsets (sub-circles) prepared for a particular round, while any other bidder is part of only a single subset. All $n$ bidders and auctioneer initiate one round of communication, and each of them prepares $l$ copies of a $\left(r-1\right)$-partite entangled state (one for each sub-circle), where $r=\frac{n}{l}+1$. The efficiency and security\textcolor{blue}{{} }of the proposed protocol are critically analyzed. It is shown that the proposed protocol is free from the collusion attacks that are possible on the existing schemes of quantum sealed-bid auction. Further, it is observed that the security against collusion attack increases with the increase in $l$, but that reduces the complexity (number of entangled qubits in each entangled state) of the entangled states to be used and that makes the scheme scalable and implementable with the available technologies. The additional security and scalability is shown to arise due to the use of a circular structure in place of a complete-graph or tree-type structure used earlier.

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arXiv2016

Teleportation of a qubit using entangled non-orthogonal states: A comparative study

The effect of non-orthogonality of an entangled non-orthogonal state based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single qubit state using all the Bell type entangled non-orthogonal states known as quasi Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi Bell state is optimal. Further, the performance of various quasi Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice's, Bob's and to be teleported qubits), but the converse may be observed in some particular cases.

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arXiv2016

A Comment on the One Step Quantum Key Distribution Based on EPR Entanglement

Recently, in Sci. Rep. \textbf{6} (2016) 28767, Li et al., have proposed a scheme for quantum key distribution using Bell states. This comment provides a proof that the proposed scheme of Li et al., is insecure as it involves leakage of information. Further, it is also shown that all the error rates computed in the Li et al.'s paper are incorrect as the authors failed to recognize the fact that any eavesdropping effort will lead to entanglement swapping. Finally, it is established that Li et al.'s scheme can be viewed as an incrementally (but incorrectly)modified version of the existing schemes based on Goldenberg Vaidman (GV) subroutine.

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arXiv2016

Quantum cryptography over non-Markovian channels

A set of schemes for secure quantum communication are analyzed under the influence of non-Markovian channels. By comparing with the corresponding Markovian cases, it is seen that the average fidelity in all these schemes can be maintained for relatively longer periods of time. The effects of non-Markovian noise on a number of facets of quantum cryptography, such as quantum secure direct communication, deterministic secure quantum communication and their controlled counterparts, quantum dialogue, quantum key distribution, quantum key agreement, etc., have been extensively investigated. Specifically, a scheme for controlled quantum dialogue (CQD) is analyzed over damping, dephasing and depolarizing non-Markovian channels, and subsequently, the effect of these non-Markovian channels on the other schemes of secure quantum communication is deduced from the results obtained for CQD. The damped non-Markovian channel causes, a periodic revival in the fidelity; while fidelity is observed to be sustained under the influence of the dephasing non-Markovian channel. The depolarizing channel, as well as the other non-Markovian channels discussed here, show that the obtained average fidelity subjected to noisy environment depends on the strength of coupling between the quantum system with its surroundings and the number of rounds of quantum communication involved in a particular scheme.

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arXiv2016

Lower order and higher order entanglement in $87Rb$ $5S-5P-5D$ hyperfine manifold modeled as a four-wave mixing process

Possibilities of generation of lower order and higher order intermodal entanglement in 87Rb 5S-5P-5D hyperfine manifold are rigorously investigated using Sen-Mandal perturbative technique by showing the equivalence of the system with the four-wave mixing (FWM) process. The investigation has revealed that for a set of experimentally realizable/relevant parameters we can observe lower order and higher order intermodal entanglement between pump and signal modes, signal and idler modes, and idler and pump modes in a FWM process associated with the 87Rb 5S-5P-5D hyperfine manifold. In addition, trimodal entanglement involving pump, signal and idler modes is also reported.

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arXiv2016

Quasiprobability distributions in open quantum systems: spin-qubit systems

Quasiprobability distributions (QDs) in open quantum systems are investigated for $SU(2)$, spin like systems, having relevance to quantum optics and information. In this work, effect of both quantum non-demolition (QND) and dissipative open quantum systems, on the evolution of a number of spin QDs are investigated. Specifically, compact analytic expressions for the $W$, $P$, $Q$, and $F$ functions are obtained for some interesting single, two and three qubit states, undergoing general open system evolutions. Further, corresponding QDs are reported for an N qubit Dicke model and a spin-1 system. The existence of nonclassical characteristics are observed in all the systems investigated here. The study leads to a clear understanding of quantum to classical transition in a host of realistic physical scenarios. Variation of the amount of nonclassicality observed in the quantum systems, studied here,are also investigated using nonclassical volume.

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arXiv2016

Tomograms for open quantum systems: in(finite) dimensional optical and spin systems

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, the quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.

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arXiv2016

Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?

In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford's law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, applicability of Benford's law has been hardly tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford's distribution in the extrasolar world using Kepler data for exoplanets. The investigation has revealed the presence of Benford's distribution in various physical properties of these exoplanets. Further, Benford goodness parameters are computed to provide a quantitative measure of coincidence of real data with the ideal values obtained from Benford's distribution. The quantitative analysis and the plots have revealed that several physical parameters associated with the exoplanets (e.g., mass, volume, density, orbital semi-major axis, orbital period, and radial velocity) nicely follow Benford's distribution, whereas some physical parameters (e.g., total proper motion, stellar age and stellar distance) moderately follow the distribution, and some others (e.g., longitude, radius, and effective temperature) do not follow Benford's distribution. Further, some specific comments have been made on the possible generalizations of the obtained result, its potential applications in analyzing data-set of candidate exoplanets, and how interested readers can perform similar investigations on other interesting data-sets.

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arXiv2016

Asymmetric Quantum Dialogue in Noisy Environment

A notion of asymmetric quantum dialogue (AQD) is introduced. Conventional protocols of quantum dialogue are essentially symmetric as both the users (Alice and Bob) can encode the same amount of classical information. In contrast, the scheme for AQD introduced here provides different amount of communication powers to Alice and Bob. The proposed scheme, offers an architecture, where the entangled state and the encoding scheme to be shared between Alice and Bob depends on the amount of classical information they want to exchange with each other. The general structure for the AQD scheme has been obtained using a group theoretic structure of the operators introduced in (Shukla et al., Phys. Lett. A, 377 (2013) 518). The effect of different types of noises (e.g., amplitude damping and phase damping noise) on the proposed scheme is investigated, and it is shown that the proposed AQD is robust and uses optimized amount of quantum resources.

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arXiv2016

Hierarchical Joint Remote State Preparation in Noisy Environment

A novel scheme for quantum communication having substantial applications in practical life is designed and analyzed. Specifically, we have proposed a hierarchical counterpart of the joint remote state preparation (JRSP) protocol, where two senders can jointly and remotely prepare a quantum state. One sender has the information regarding amplitude, while the other one has the phase information of a quantum state to be jointly prepared at the receiver's port. However, there exists a hierarchy among the receivers, as far as powers to reconstruct the quantum state is concerned. A 5-qubit cluster state has been used here to perform the task. Further, it is established that the proposed scheme for hierarchical JRSP (HJRSP) is of enormous practical importance in critical situations involving defense and other sectors, where it is essential to ensure that an important decision/order that can severely affect a society or an organization is not taken by a single person, and once the order is issued all the receivers don't possess an equal right to implement it. Further, the effect of different noise models (e.g., amplitude damping (AD), phase damping (PD), collective noise and Pauli noise models) on the HJRSP protocol proposed here is investigated. It is found that in AD and PD noise models a higher power agent can reconstruct the quantum state to be remotely prepared with higher fidelity than that done by the lower power agent(s). In contrast, the opposite may happen in the presence of collective noise models. We have also proposed a scheme for probabilistic HJRSP using a non-maximally entangled 5-qubit cluster state.

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arXiv2016

A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols

The effect of noise on various protocols of secure quantum communication has been studied. Specifically, we have investigated the effect of amplitude damping, phase damping, squeezed generalized amplitude damping, Pauli type as well as various collective noise models on the protocols of quantum key distribution, quantum key agreement,quantum secure direct quantum communication and quantum dialogue. From each type of protocol of secure quantum communication, we have chosen two protocols for our comparative study; one based on single qubit states and the other one on entangled states. The comparative study reported here has revealed that single-qubit-based schemes are generally found to perform better in the presence of amplitude damping, phase damping, squeezed generalized amplitude damping noises, while entanglement-based protocols turn out to be preferable in the presence of collective noises. It is also observed that the effect of noise entirely depends upon the number of rounds of quantum communication involved in a scheme of quantum communication. Further, it is observed that squeezing, a completely quantum mechanical resource present in the squeezed generalized amplitude channel, can be used in a beneficial way as it may yield higher fidelity compared to the corresponding zero squeezing case.

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arXiv2016

Analysis and improvement of Tian-Zhang-Li voting protocol based on controlled quantum teleportation

Recently Tian, Zhang and Li (TZL) have proposed a protocol for voting based on controlled quantum teleportation (Int. J. Theor. Phys. DOI 10.1007/s10773-015-2868-8). We have critically analyzed the protocol and have shown that it's neither efficient nor secure. Further, it is shown that in the TZL protocol, the scrutineer Charlie does not have the required control over the voting process. Apart from showing the limitations of TZL protocol, two improved protocols for quantum voting along the line of TZL protocol are proposed here. One of the proposed protocols is designed using a standard scheme of controlled deterministic secure quantum communication, and the other one is designed using the idea of quantum cryptographic switch which uses a technique known as permutation of particles (PoP). A few possible alternative approaches to accomplish the same task have also been discussed. Further, the efficiencies of the proposed protocols are reported, and it is shown that the proposed protocols are free from the limitations of the TZL protocol, and they are more efficient than the TZL protocol.

quant-ph↗

arXiv2015

Linear and nonlinear quantum Zeno and anti-Zeno effects in a nonlinear optical coupler

Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear ($χ^{\left(2\right)}$) waveguides that are interacting with each other via the evanescent waves. Both the waveguides operate under second harmonic generation. However, to study quantum Zeno and anti-Zeno effects one of them is considered as the system and the other one is considered as the probe. Considering all the fields involved as weak, a completely quantum mechanical description is provided, and the analytic solutions of Heisenberg's equations of motion for all the field modes are obtained using a perturbative technique. Photon number statistics of the second harmonic mode of the system is shown to depend on the presence of the probe, and this dependence is considered as quantum Zeno and anti-Zeno effects. Further, it is established that as a special case of the momentum operator for $χ^{\left(2\right)}-χ^{\left(2\right)}$ symmetric coupler we can obtain momentum operator of $χ^{\left(2\right)}-χ^{\left(1\right)}$ asymmetric coupler with linear ($χ^{\left(1\right)}$) waveguide as the probe, and in such a particular case, the expressions obtained for Zeno and anti-Zeno effects with nonlinear probe (which we referred to as nonlinear quantum Zeno and anti-Zeno effects) may be reduced to the corresponding expressions with linear probe (which we referred to as the linear quantum Zeno and anti-Zeno effects). Linear and nonlinear quantum Zeno and anti-Zeno effects are rigorously investigated, and it is established that in the stimulated case, we may switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the system or probe.

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arXiv2015

Higher order two-mode and multi-mode entanglement in Raman processes

The existence of higher order entanglement in the stimulated and spontaneous Raman processes is established using the perturbative solutions of the Heisenberg equations of motion for various field modes that are obtained using the Sen-Mandal technique and a fully quantum mechanical Hamiltonian that describes the stimulated and spontaneous Raman processes. Specifically, the perturbative Sen-Mandal solutions are exploited here to show the signature of the higher order two-mode and multi-mode entanglement. In some special cases, we have also observed higher order entanglement in the partially spontaneous Raman processes. Further, it is shown that the depth of the nonclassicality indicators (parameters) can be manipulated by the specific choice of coupling constants, and it is observed that the depth of nonclassicality parameters increases with the order.

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arXiv2015

Which verification qubits perform best for secure communication in noisy channel?

In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy environment (e.g., in amplitude damping, phase damping, collective dephasing and collective rotation noise channels) by comparing the decoy-qubit assisted schemes of secure quantum communication that use single qubit states as decoy qubits with the schemes that use entangled states as decoy qubits. Our study reveals that the single qubit assisted scheme perform better in some noisy environments, while some entangled qubits assisted schemes perform better in other noisy environments. Specifically, single qubits assisted schemes perform better in amplitude damping and phase damping noisy channels, whereas a few Bell-state-based decoy schemes are found to perform better in the presence of the collective noise. Thus, if the kind of noise present in a communication channel (i.e., the characteristics of the channel) is known or measured, then the present study can provide the best choice of decoy qubits required for implementation of schemes of secure quantum communication through that channel.

quant-ph↗

arXiv2015

Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler

Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler are studied. The asymmetric nonlinear optical coupler is composed of a linear waveguide ($χ^{\left(1\right)}$) and a nonlinear waveguide ($χ^{\left(2\right)}$) interacting with each other through the evanescent waves. The nonlinear waveguide has quadratic nonlinearity and it operates under second harmonic generation. A completely quantum mechanical description is used to describe the system. The closed form analytic solutions of Heisenberg's equations of motion for the different field modes are obtained using Sen-Mandal perturbative approach. In the coupler, the linear waveguide acts as a probe on the system (nonlinear waveguide). The effect of the presence of the probe (linear waveguide) on the photon statistics of the second harmonic mode of the system is considered as quantum Zeno and anti-Zeno effects. Further,it is also shown that in the stimulated case, it is easy to switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the asymmetric coupler

quant-ph↗

arXiv2015

Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $τ$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP) and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance $D$ for a fixed value of both the depth $τ$ and NP in the whole range $[0,1]$ of their values, as well as the NP for a given value of $τ$ such that $τ>0.3154$. Conversely, pure states are the most nonclassical single-qubit states with respect to $τ$ for a given $D$, NP versus $D$, and $τ$ versus NP. We also show the "relativity" of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states.

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