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 ($\chi^{\left(1\right)}$) and a nonlinear waveguide ($\chi^{\left(2\right)}$) 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 couplerComment: 7 pages. This work was presented in the International Conference on Optics and Photonics 2015,Kolkata, Indi

Applications of quantum cryptographic switch: Various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles

Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using $n$-qubit ($n\geq3$) entanglement. Specially, a large number of schemes for bidirectional controlled state teleportation are proposed using $m$-qubit entanglement ($m\in\{5,6,7\}$). Here, we propose a set of protocols to illustrate that it is possible to realize all these tasks related to controlled quantum communication using only Bell states and permutation of particles (PoP). As the generation and maintenance of a Bell state is much easier than a multi-partite entanglement, the proposed strategy has a clear advantage over the existing proposals. Further, it is shown that all the schemes proposed here may be viewed as applications of the concept of quantum cryptographic switch which was recently introduced by some of us. The performances of the proposed protocols as subjected to the amplitude damping and phase damping noise on the channels are also discussed.Comment: 12 pages, 3 figure

Quantum e-commerce: A comparative study of possible protocols for online shopping and other tasks related to e-commerce

A set of quantum protocols for online shopping is proposed and analyzed to establish that it is possible to perform secure online shopping using different types of quantum resources. Specifically, a single photon based, a Bell state based and two 3-qubit entangled state based quantum online shopping schemes are proposed. The Bell state based scheme, being a completely orthogonal state based protocol, is fundamentally different from the earlier proposed schemes which were based on conjugate coding. One of the 3-qubit entangled state based scheme is build on the principle of entanglement swapping which enables us to accomplish the task without transmission of the message encoded qubits through the channel. Possible ways of generalizing the entangled state based schemes proposed here to the schemes which use multiqubit entangled states is also discussed. Further, all the proposed protocols are shown to be free from the limitations of the recently proposed protocol of Huang et al. (Quantum Inf. Process. 14, 2211-2225, 2015) which allows the buyer (Alice) to change her order at a later time (after initially placing the order and getting it authenticated by the controller). The proposed schemes are also compared with the existing schemes using qubit efficiency.Comment: It's shown that quantum e-commerce is not a difficult task, and it can be done in various way

Kak's three-stage protocol of secure quantum communication revisited: Hitherto unknown strengths and weaknesses of the protocol

Kak's three-stage protocol for quantum key distribution is revisited with special focus on its hitherto unknown strengths and weaknesses. It is shown that this protocol can be used for secure direct quantum communication. Further, the implementability of this protocol in the realistic situation is analyzed by considering various Markovian noise models. It is found that the Kak's protocol and its variants in their original form can be implemented only in a restricted class of noisy channels, where the protocols can be transformed to corresponding protocols based on logical qubits in decoherence free subspace. Specifically, it is observed that Kak's protocol can be implemented in the presence of collective rotation and collective dephasing noise, but cannot be implemented in its original form in the presence of other types of noise, like amplitude damping and phase damping noise. Further, the performance of the protocol in the noisy environment is quantified by computing average fidelity under various noise models, and subsequently a set of preferred states for secure communication in noisy environment have also been identified.Comment: Kak's protocol is not suitable for quantum cryptography in presence of nois

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.Comment: 17 pages, 10 figure

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 ($\chi^{\left(2\right)}$) 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 $\chi^{\left(2\right)}-\chi^{\left(2\right)}$ symmetric coupler we can obtain momentum operator of $\chi^{\left(2\right)}-\chi^{\left(1\right)}$ asymmetric coupler with linear ($\chi^{\left(1\right)}$) 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.Comment: 13 pages 9 figure

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.Comment: 24 pages, 6 figure

Continuous variable controlled quantum dialogue and secure multiparty quantum computation

A continuous variable controlled quantum dialogue scheme is proposed. The scheme is further modified to obtain two other protocols of continuous variable secure multiparty computation. The first one of these protocols provides a solution of two party socialist millionaire problem, while the second protocol provides a solution for a special type of multi-party socialist millionaire problem which can be viewed as a protocol for multiparty quantum private comparison. It is shown that the proposed scheme of continuous variable controlled quantum dialogue can be performed using bipartite entanglement and can be reduced to obtain several other two and three party cryptographic schemes in the limiting cases. The security of the proposed scheme and its advantage over corresponding discrete variable counterpart are also discussed. Specifically, the ignorance of an eavesdropper in the proposed scheme is shown to be very high compared with corresponding discrete variable scheme and thus the present scheme is less prone to information leakage inherent with the discrete variable quantum dialogue based schemes.It is further established that the proposed scheme can be viewed as a continuous variable counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.Comment: Quantum dialogue and its application in the continuous variable scenario is studied in detai

A General Method for Selecting Quantum Channel for Bidirectional Controlled State Teleportation and Other Schemes of Controlled Quantum Communication

Recently, a large number of protocols for bidirectional controlled state teleportation (BCST) have been proposed using $n$-qubit entangled states ($n\in\{5,6,7\}$) as quantum channel. Here, we propose a general method of selecting multi-qubit $(n>4)$ quantum channels suitable for BCST and show that all the channels used in the existing protocols of BCST can be obtained using the proposed method. Further, it is shown that the quantum channels used in the existing protocols of BCST forms only a negligibly small subset of the set of all the quantum channels that can be constructed using the proposed method to implement BCST. It is also noted that all these quantum channels are also suitable for controlled bidirectional remote state preparation (CBRSP). Following the same logic, methods for selecting quantum channels for other controlled quantum communication tasks, such as controlled bidirectional joint remote state preparation (CJBRSP) and controlled quantum dialogue, are also provided.Comment: 8 pages, no figur