Banerjee, Subashish

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A (B) to have a winning probability more than player B (A). Significance of the game strategy in information theory and physical applications are also discussed.

Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties of the two modes of radiation. The nonunitary, noncyclic path in the state space may be realized through the same control parameters which control the purity/mixedness and entanglement. We show analytically that the geometric phase is related to concurrence in certain region of the parameter space. We further show that the rate of change of the geometric phase reveals its resilience to fluctuations only for pure Bell type states. Lastly, the derivative of the geometric phase carries information on both purity/mixedness and entanglement/separability. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.

The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control leads to a faster decay of entanglement. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dynamic decoupling control has the expected effect of slowing down the decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath under a nondemolition interaction. However, nontrivial phenomena are observed when a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is subject to decoupling pulses. The most striking of these reflects the resonance fluorescence scenario, in that an increase in the pulse strength decreases decoherence but also speeds up the sudden death of entanglement. This demonstrates that the behavior of decoherence and entanglement in time can be qualitatively different in the strong-coupling non-Markovian regime. © 2012 American Physical Society.

Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate nonclassicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of nonclassicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness. © 2011 American Physical Society.

We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP divisibility of the map, i.e., appearance of a not-completely positive intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation and thus to a momentary noninvertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP divisibility [Hall, Phys. Rev. A 89, 042120 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042120], which does not require optimization but requires normalization to handle the singularity, and another method, based on distinguishability [Breuer Phys. Rev. Lett. 103, 210401 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.210401], which requires optimization but is insensitive to the singularity.

In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can’t replace the noisy communication channel with an ideal one, but her eavesdropping channel itself remains noiseless. Here, we point out such a situation, where the security of the ping–pong protocol (modified to a key distribution scheme) against a noise-restricted adversary improves under a non-unital noisy channel, but deteriorates under unital channels. This highlights the surprising fact that, contrary to the conventional expectation, noise can be helpful to quantum information processing. Furthermore, we point out that the measurement outcome data in the context of the non-unital channel can’t be simulated by classical noise locally added by the legitimate users.

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral Bd, Bs and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter D[n] closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in Bd and Bs systems.

The violation of Leggett-Garg-type inequalities (LGtIs) is studied on a two-level atom, driven by an external field in the presence of a squeezed thermal reservoir. The violations are observed in the underdamped regime where the spontaneous transition rate is much smaller compared to the Rabi frequency. An increase in thermal effects is found to decrease the extent of violation as well as the time over which the violation lasts. With the increase in the value of the squeezing parameter the extent of violation of LGtIs is seen to reduce. The violation of LGtIs is favored by an increase in the driving frequency. Further, the interplay of the degree of violation and strength of the measurements is studied. It is found that the maximum violation occurs for ideal projective measurements.

Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non-Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non-unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed.

Gravity induced neutrino-antineutrino oscillations are studied in the context of one- and two-flavor scenarios. This allows one to investigate the particle-antiparticle correlations in two and four level systems, respectively. Flavor entropy is used to probe the entanglement in the system. The well known witnesses of nonclassicality such as Mermin and Svetlichny inequalities are investigated. Since the extent of neutrino-antineutrino oscillation is governed by the strength of the gravitational field, the behavior of nonclassicality shows interesting features as one varies the strength of the gravitational field. Specifically, the suppression of the entanglement with the increase of the gravitational field is observed which is witnessed in the form of decrease in the flavor entropy of the system. The features of the Mermin and the Svetlichny inequalities allow one to make statements about the degeneracy of neutrino mass eigenstates.