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Subhashish Banerjee

Publications and source records attributed to Subhashish Banerjee.

At least 163 records · Page 9Linked to original sources
arXiv2013

Entanglement in the Grover's Search Algorithm

Quantum Algorithms have long captured the imagination of computer scientists and physicists primarily because of the speed up achieved by them over their classical counterparts using principles of quantum mechanics. Entanglement is believed to be the primary phenomena behind this speed up. However their precise role in quantum algorithms is yet unclear. In this article, we explore the nature of entanglement in the Grover's search algorithm. This algorithm enables searching of elements from an unstructured database quadratically faster than the best known classical algorithm. Geometric measure of entanglement has been used to quantify and analyse entanglement across iterations of the algorithm. We reveal how the entanglement varies with increase in the number of qubits and also with the number of marked or solution states. Numerically, it is seen that the behaviour of the maximum value of entanglement is monotonous with the number of qubits. Also, for a given value of the number of qubits, a change in the marked states alters the amount of entanglement. The amount of entanglement in the final state of the algorithm has been shown to depend solely on the nature of the marked states. Explicit analytical expressions are given showing the variation of entanglement with the number of iterations and the global maximum value of entanglement attained across all iterations of the algorithm.

quant-ph↗
arXiv2013

Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect

Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here, we show that when a quantum system interacts with two competing environments there can be enhancement of geometric phase. This effect is akin to Parrondo like effect on the geometric phase which results from quantum frustration of decoherence. Our result suggests that the mechanism of two competing decoherence can be useful in fault-tolerant holonomic quantum computation.

quant-ph↗
arXiv2013

Decoherence free Bd and Bs meson systems

We study the impact of decoherence on B meson systems with specific emphasis on Bs. For consistency we also study the Bd mesons based on the most recent data. We find that the Bd mesons are 34 sigma away from total decoherence, while the Bs mesons are seen to be upto 31sigma away from total decoherence. Thus, our results prove, with experimental verity, that neutral meson systems are free from decoherence effects. Therefore, this provides a very useful laboratory for testing the foundations of quantum mechanics.

hep-ph↗
arXiv2013

Controllable quantum correlations of two-photon states generated using classically driven three-level atoms

We investigate the dynamics of two-photon correlations generated by the interaction of a three-level atom in the $Ξ$, $Λ$ or V configuration, with two classical external driving fields, under the rotating-wave approximation, in the presence of level decays. Using the example of a rubidium atom in each configuration, with field strengths validating the single-photon approximation, we compute measurement based correlations, such as measurement induced disturbance (MID), quantum discord (QD), and quantum work deficit (WD), and compare the results with that of quantum entanglement (concurrence). Certain correlation properties observed are generic, model independent and consistent with known results, e.g., MID is an upper bound on QD, QD and WD are monotonic, and the generic correlation behavior is strongly affected by the purity of the photon states. We observe that the qualitative hierarchy, monotonicity and steady-state behavior of the correlations can be controlled by the choice of parameters such as atomic decay constants and external driving field strengths. We point out how particular configurations are better suited at generating monotonic correlations in specific regimes and how the steady-state correlation behavior and hierarchy are affected by the population dynamics of the density matrix for different parameters. The possibility of using well studied quantum optical systems such as the three-level atom to generate, characterize and parametrically control mixed state quantum correlations establishes an important step in the direction of their implementation in quantum information tasks.

quant-ph↗
arXiv2012

The operator sum-difference representation for quantum maps: application to the two-qubit amplitude damping channel

On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and higher order polynomials, the eigenvalue problem and the associated characteristic equation for a general noise dynamics in dimension $d$ via the Choi-Jamiolkowski approach cannot be solved in general via radicals. We provide a way around this impasse by decomposing the Choi matrix into simpler, not necessarily positive, Hermitian operators that are diagonalizable via radicals, which yield a set of `positive' and `negative' Kraus operators. The price to pay is that the sufficient number of Kraus operators is $d^4$ instead of $d^2$, sufficient in the Kraus representation. We consider various applications of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel, the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath; defining the maximally dephasing and purely dephasing components of the channel in the new representation, and studying their entanglement breaking and broadcast properties.

quant-ph↗
arXiv2012

An Operational Meaning of Discord in terms of Teleportation Fidelity

Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of non-classical correlation of an arbitrary quantum system in terms of its minimal distance from the set of classical states, in terms of teleportation fidelity for general two qubit and $d \otimes d$ dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two qubit state must violate the Bell inequality. This is illustrated by an open system model of a dissipative two qubit. For the $d \otimes d$ dimensional states the lower bound of discord is shown to be obtainable from an experimentally measurable witness operator.

quant-ph↗
arXiv2012

Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.

quant-ph↗
arXiv2012

Entanglement generation in spatially separated systems using quantum walk

We present a novel scheme to generate entanglement between two spatially separated systems. The scheme makes use of spatial entanglement generated by a single-particle quantum walk which is used to entangle two spatially separated, not necessarily correlated, systems. This scheme can be used to entangle any two systems which can interact with the spatial modes entangled during the quantum walk evolution. A notable feature is that we can control the quantum walk dynamics and its ability to localize leads to a substantial control and improvement in the entanglement output.

quant-ph↗
arXiv2012

q-deformed logistic map with delay feedback

The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the map and its bifurcation scheme is analyzed as a function of the deformation and delay feedback parameters. Chaos is suppressed in a certain region of deformation and feedback parameter space. The steady state obtained by delay feedback is maintained in one type of deformation while chaotic behavior is recovered in another type with increasing delay.

nlin.CD↗
arXiv2012

Geometric Phase: a Diagnostic Tool for Entanglement

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.

quant-ph↗
arXiv2011

A study of Quantum Correlations in Open Quantum Systems

In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

quant-ph↗
arXiv2011

The quantum cryptographic switch

We illustrate using a quantum system the principle of a cryptographic switch, in which a third party (Charlie) can control to a continuously varying degree the amount of information the receiver (Bob) receives, after the sender (Alice) has sent her information. Suppose Charlie transmits a Bell state to Alice and Bob. Alice uses dense coding to transmit two bits to Bob. Only if the 2-bit information corresponding to choice of Bell state is made available by Charlie to Bob can the latter recover Alice's information. By varying the information he gives, Charlie can continuously vary the information recovered by Bob. The performance of the protocol subjected to the squeezed generalized amplitude damping channel is considered. We also present a number of practical situations where a cryptographic switch would be of use.

quant-ph↗
arXiv2011

An information theoretic study of number-phase complementarity in a four level atomic system

We study number-phase uncertainty in a laser-driven, effectively four-level atomic system under electromagnetically induced transparency (EIT) and coherent population trapping (CPT). Uncertainty is described using (entropic) knowledge of the two complementary variables, namely, number and phase, where knowledge is defined as the relative entropy with respect to a uniform distribution. In the regime where the coupling and probe lasers are approximately of equal strength, and the atom exists in a CPT state, there is coherence between the ground states, and correspondingly large phase knowledge and lower number knowledge. The situation is the opposite in the case where coupling laser is much stronger and the atom exists in an EIT state. We study these effects also in the presence of a higher-order nonlinear absorption, which is seen to produce a dephasing effect.

quant-ph↗
arXiv2011

Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord

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 non-classicality 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 the trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of non-classicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.

quant-ph↗
arXiv2011

Parrondo's game using a discrete-time quantum walk

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.

quant-ph↗
arXiv2010

Entanglement Dynamics in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Quantum Nondemolition interaction

We analyze the dynamics of entanglement in a two-qubit system interacting with an initially squeezed thermal environment via a quantum nondemolition system-reservoir interaction, with the system and reservoir assumed to be initially separable. We compare and contrast the decoherence of the two-qubit system in the case where the qubits are mutually close-by (`collective regime') or distant (`localized regime') with respect to the spatial variation of the environment. Sudden death of entanglement (as quantified by concurrence) is shown to occur in the localized case rather than in the collective case, where entanglement tends to `ring down'. A consequence of the QND character of the interaction is that the time-evolved fidelity of a Bell state never falls below $1/\sqrt{2}$, a fact that is useful for quantum communication applications like a quantum repeater. Using a novel quantification of mixed state entanglement, we show that there are noise regimes where even though entanglement vanishes, the state is still available for applications like NMR quantum computation, because of the presence of a pseudo-pure component.

quant-ph↗
arXiv2010

A thermodynamic geometric study of Rényi and Tsallis entropies

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection between statistical mechanics and the corresponding Riemannian geometry. The form of the entropy used commonly is the Shannon entropy. However, for modelling complex systems, it is often useful to make use of entropies such as the Rényi and Tsallis entropies. We consider, here, Shannon, Rényi, Tsallis, Abe and structural entropies, for our analysis. We focus on one, two and three particle thermally excited configurations. We find that statistical pair correlation functions, determined by the components of the covariant metric tensor of the underlying thermodynamic geometry, associated with the various entropies have well defined, definite expressions, which may be extended for arbitrary finite particle systems. In all cases, we find a non-degenerate intrinsic Riemannian manifold. In particular, any finite particle system described in terms of Rényi, Tsallis, Abe and structural entropies, always corresponds to an interacting statistical system, thereby highlighting their importance in the study of complex systems. On the other hand, a statistical description by the Gibbs-Shannon entropy corresponds to a non-interacting system.

cond-mat.stat-mech↗