arXiv subjects

A. R. Usha Devi

Publications and source records attributed to A. R. Usha Devi.

At least 55 records · Page 3Linked to original sources

arXiv2011

Quantumness of correlations and entanglement

Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by employing linear maps associated with generalized projective measurements. A generalized measurement corresponds to a quantum operation mapping a density matrix to another density matrix, preserving its positivity, hermiticity and traceclass. The Positive Operator Valued Measure (POVM) -- employed earlier in the literature to optimize the measures of classical/quatnum correlations -- correspond to completely positive (CP) maps. The other class, the not completely positive (NCP) maps, are investigated here, in the context of measurements, for the first time. It is shown that that such NCP projective maps provide a new clue to the understanding the quantumness of correlations in a general setting. Especially, the separability-classicality dichotomy gets resolved only when both the classes of projective maps (CP and NCP) are incorporated as optimizing measurements. An explicit example of a separable state -- exhibiting non-zero quantumn discord when possible optimizing measurements are restricted to POVMs -- is re-examined with this extended scheme incorporating NCP projective maps to elucidate the power of this approach.

quant-ph↗

arXiv2011

Quantum dynamical maps and Markovianity

It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if NCP) avataras of the intermediate dynamics. This is brought out based on A and B dynamical maps - without resorting to Master equation approach. The choice of tensor product form for the global initial state points towards the system-environment interaction dynamics as the sole cause for Markovianity/non-Markovianity. A succinct summary of the results is given in the form of a table.

quant-ph↗

arXiv2011

Majorana representation of symmetric multiqubit states

As early as 1932, Majorana had proposed that a pure permutation symmetric state of N spin- 1 2 particles can be represented by N spinors, which correspond geometrically to N points on the Bloch sphere. Several decades after its conception, the Majorana representation has recently attracted a great deal of attention in connection with multiparticle entanglement. A novel use of this represen- tation led to the classification of entanglement families of permutation symmetric qubits - based on the number of distinct spinors and their arrangement in constituting the multiqubit state. An elegant approach to explore how correlation information of the whole pure symmetric state gets imprinted in its parts is developed for specific entanglement classes of symmetric states. More- over, an elegant and simplified method to evaluate geometric measure of entanglement in N-qubit states obeying exchange symmetry has been developed based on the distribution of the constituent Majorana spionors over the unit sphere. Multiparticle entanglement being a key resource in sev- eral quantum information processing tasks, its deeper understanding is essential. In this review, we present a detailed description of the Majorana representation of pure symmetric states and its applicability in investigating various aspects of multiparticle entanglement.

quant-ph↗

arXiv2011

Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity

Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open system evolution of quantum systems. A canonical structure of the A-map is introduced here. It is shown that this canonical A-map enables us to investigate if the dynamics is completely positive (CP) or non-completely positive (NCP) in an elegant way and hence, it subsumes the basic results on open system dynamics. Identifying memory effects in open system evolution is gaining increasing importance recently and here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization - though not related directly - to the fidelity difference criterion proposed recently. Three typical examples of open system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics - which corresponds to a NCP dynamical map - are investigated by employing both the relative entropy difference and fidelity difference tests of non-Markovianity. The two qubit initial states are chosen to be (i) a pure entangled state, (ii) theWerner state, which exemplifies both entangled and separable states of qubits, depending on a real parameter, and (3) a separable mixed state. Both the relative entropy and fidelity criteria offer a nice display of how non-Markovianity manifests in all the three examples.

quant-ph↗

arXiv2010

Spin Squeezing and Quantum Correlations

Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.

quant-ph↗

arXiv2010

Entropic characterization of Separability in Gaussian states

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q tending to infinity) than that obtained from the corresponding von Neumann conditional entropy (q = 1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.

quant-ph↗

arXiv2010

The thermostatistical aspect of Werner-type states and quantum entanglement

A general Werner-type state is studied from two viewpoints: (i) an application of dynamical interaction of the objective system with its environment, represented by a unital positive operator-valued measure (POVM), which ensures increase of entropy, makes the system evolve from an initial pure state to a mixed state of the Werner type, and (ii) the space of the objective system is constrained to have a given value of the fidelity. Then, the maximum entropy principle is shown to yield the Werner-type state as a canonical ensemble with the projector Hamiltonian. This novel observation is illustrated by examples of bipartite systems, the separability criteria on which are given in terms of the values of temperature. The present viewpoint may cast light on relevance of thermostatistics to the physics of quantum entanglement. In addition, the POVM scheme presented here offers a way of experimentally generating the Werner-type thermal states.

cond-mat.stat-mech↗

arXiv2009

Loss of exchange symmetry in multiqubit states under Ising chain evolution

Keeping in view the exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that Ising type Hamiltonian does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically, we show that all N-qubit states (N greater than or equal to 5) obeying permutation symmetry lose their symmetry after evolution with one dimensional Ising chain with nearest neighbor interactions. Among 4-qubit symmetric pure states, only W type states retain their symmetry under time evolution with Ising Hamiltonian.

quant-ph↗

arXiv2009

Quantum target detection using entangled photons

We investigate performances of pure continuous variable states in discriminating thermal and identity channels by comparing their M-copy error probability bounds. This offers us a simplified mathematical analysis for quantum target detection with slightly modified features: the object -- if it is present -- perfectly reflects the signal beam irradiating it, while thermal noise photons are returned to the receiver in its absence. This model facilitates us to obtain analytic results on error-probability bounds i.e., the quantum Chernoff bound and the lower bound constructed from the Bhattacharya bound on M-copy discrimination error-probabilities of some important quantum states, like photon number states, N00N states, coherent states and the entangled photons obtained from spontaneous parametric down conversion (SPDC). Comparing the $M$-copy error-bounds, we identify that N00N states indeed offer enhanced sensitivity than the photon number state system, when average signal photon number is small compared to the thermal noise level. However, in the high signal-to-noise scenario, N00N states fail to be advantageous than the photon number states. Entangled SPDC photon pairs too outperform conventional coherent state system in the low signal-to-noise case. On the other hand, conventional coherent state system surpasses the performance sensitivity offered by entangled photon pair, when the signal intensity is much above that of thermal noise. We find an analogous performance regime in the lossy target detection (where the target is modeled as a weakly reflecting object) in a high signal-to-noise scenario.

quant-ph↗

arXiv2008

A scheme for amplification and discrimination of photons

A scheme for exploring photon number amplification and discrimination is presented based on the interaction of a large number of two-level atoms with a single mode radiation field. The fact that the total number of photons and atoms in the excited states is a constant under time evolution in Dicke model is exploited to rearrange the atom-photon numbers. Three significant predictions emerge from our study: Threshold time for initial exposure to photons, time of perception (time of maximum detection probability), and discrimination of first few photon states.

quant-ph↗

arXiv2008

Distinctive subdynamic features of bipartite systems

There are several important bipartite systems of great interest in condensed matter physics and in quantum information science. In condensed matter systems, the subsystems are examined traditionally by using the Green function and mean-field-like methods based on the Heisenberg representation. In quantum information science, the subsystems are handled by composite density matrix, its marginals describing the subsystems, and the Kraus representation to elucidate the subsystem properties. In this work, a relationship is first established between the two techniques which appear to be distinct at first sight. This will be illustrated in detail by presenting the two methods in the case of the celebrated exactly soluable Jaynes - Cummings model (1963) of a two-state atom interacting with a one-mode quantized electromagnetic field. The dynamics of this system was treated in the Heisenberg representation by Ackerhalt and Rzazewski (1975). We present here the corresponding subdynamics using Kraus representation. A relationship between the two approaches is established and the relative merits of the two techniques are discussed in elucidating the distinctive features of the subdynamics. The striking effects of interaction and entanglement are made transparent in two illustrative examples: the transformations that manifest in non-interacting number and spin representations due to interactions in their respective subspaces.

quant-ph↗

arXiv2008

Quantum Mechanical Basis of Vision

The two striking components of retina, i.e., the light sensitive neural layer in the eye, by which it responds to light are (the three types of) color sensitive Cones and color insensitive Rods (which outnumber the cones 20:1). The interaction between electromagnetic radiation and these photoreceptors (causing transitions between cis- and trans- states of rhodopsin molecules in the latter) offers a prime example of physical processes at the nano-bio interface. After a brief review of the basic facts about vision, we propose a quantum mechanical model (paralleling the Jaynes-Cummings model (JCM) of interaction of light with matter) of early vision describing the interaction of light with the two states of rhodopsin mentioned above. Here we model the early essential steps in vision incorporating, separately, the two well-known features of retinal transduction (converting light to neural signals): small numbers of cones respond to bright light (large number of photons) and large numbers of rods respond to faint light (small number of photons) with an amplification scheme. An outline of the method of solution of these respective models based on quantum density matrix is also indicated. This includes a brief overview of the theory, based on JCM, of signal amplification required for the perception of faint light. We envision this methodology, which brings a novel quantum approach to modeling neural activity, to be a useful paradigm in developing a better understanding of key visual processes than is possible with currently available models that completely ignore quantum effects at the relevant neural level.

q-bio.NC↗

arXiv2008

Generalized information theoretic measure to discern the quantumness of correlations

A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in special cases and it vanishes for separable states - a feature not captured by the measures proposed earlier. It is found that an optimal generalized measurement on one of the parts leaves the overall state in its closest separable form, which shares the same marginal for the other part, implying that quantumness is non-zero for all entangled bipartite states and it serves as an upper bound to the relative entropy of entanglement.

quant-ph↗

arXiv2007

Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach

We employ conditional Tsallis q entropies to study the separability of symmetric one parameter W and GHZ multiqubit mixed states. The strongest limitation on separability is realized in the limit q-->infinity, and is found to be much superior to the condition obtained using the von Neumann conditional entropy (q=1 case). Except for the example of two qubit and three qubit symmetric states of GHZ family, the $q$-conditional entropy method leads to sufficient - but not necessary - conditions on separability.

quant-ph↗

arXiv2007

Distinctive features in the quantum sub-dynamics of bipartite systems

Distinctive features in the sub-dynamics of an interacting bipartite system are explored. The sub-dynamic Heisenberg operators are introduced in a novel way leading to the quasi-particle-like concept in the respective subsystems. This formulation is illustrated using the known exact solutions of the generic (Jaynes - Cummings) model of interacting bipartite system of a spin 1/2 particle and a single mode electromagnetic field (more generally, boson field). The striking effects of interaction and entanglement are reflected in the dressing of the non-interacting number and spin representations, displaying quasi-particle-like properties. This development may be at the heart of the physics of back - action discussed in the recent literature.

quant-ph↗

arXiv2007

Collective multipole-like signatures of entanglement in symmetric N-qubit systems

A cogent theory of collective multipole-like quantum correlations in symmetric multiqubit states is presented by employing SO(3) irreducible spherical tensor representation. An arbitrary bipartite division of this system leads to a family of inequalities to detect entanglement involving averages of these tensors expressed in terms of the total system angular momentum operator. Implications of this theory to the quantum nature of multipole-like correlations of all orders in the Dicke states are deduced. A selected set of examples illustrate these collective tests. Such tests detect entanglement in macroscopic atomic ensembles, where individual atoms are not accessible.

quant-ph↗

arXiv2007

A POVM view of the ensemble approach to polarization optics

Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight. With suitable choice of the Jones ensemble, various Mueller transformations - some of which have been unknown so far - are deduced. It is observed that the ensemble approach is formally identical to the positive operator valued measures (POVM) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne (Phys. Rev. A 71, 012330, (2005)) - in the context of generalized quantum measurement on single photon polarization states - that linear optics elements can be employed in setting up all possible POVMs, enables us to propose a way of realizing different types of Mueller devices.

physics.optics↗

arXiv2007

Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices

We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order inter-group covariance matrices of symmetric N-qubit systems. These conditions have a simple structure and detect entanglement in all even partitions of the symmetric multiqubit system. The observables involved are feasible experimental quantities and do not demand full state determination through quantum state tomography.

quant-ph↗