Monogamy, polygamy, and other properties of entanglement of purification

For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.Comment: 12 pages, 2 figures, Published versio

Nonexponentiality of time dependent survival probability and the fractional viscosity dependence of the rate in diffusion controlled reactions in a polymer chain

Brownian dynamics (BD) simulations have been carried out for the time dependent survival probability [Sp(t)] of donor-acceptor pairs embedded at the two ends of an ideal polymer chain. Long distance fluorescence resonance energy transfer (FRET) between the donor and the acceptor is assumed to occur via the Forster mechanism, where the transfer rate k(R) is a function of the distance (R) between the donor and acceptor. For the Rouse chain simulated here, k(R) is assumed to be given by k = kF/[1+(R/RF)6], where kF is the rate in the limit of zero separation and RF is the Forster radius. The survival probability displays a strong nonexponential decay for the short to intermediate times when RF is comparable to RM [distance at which the R2P(R) is maximum]. The nonexponentiality is also more prominent in the case of highly viscous polymer solutions. It is predicted that the FRET rate can exhibit a fractional viscosity dependence. This prediction can be tested against experiments. We have also compared the BD simulation results with the predictions of the well-known Wilemski-Fixman (WF) theory at the level of survival probability. It is found that the WF theory is satisfactory for the smaller RF values (where the rate is small). However, the agreement becomes progressively poorer as the Forster radius is increased. The latter happens even at intermediate strengths of kF. The present results suggest the need to go beyond the WF theory

Remote Creation of Quantum Coherence via Indefinite Causal Order

Quantum coherence is a prime resource in quantum computing and quantum communication. Quantum coherence of an arbitrary qubit state can be created at a remote location using maximally entangled state, local operation and classical communication. However, if there is a noisy channel acting on one side of the shared resource, then, it is not possible to create perfect quantum coherence remotely. Here, we present a method for the creation of quantum coherence at a remote location via the use of entangled state and indefinite causal order. We show this specifically for the superposition of two completely depolarizing channels, two partially depolarizing channels and one completely depolarizing channel along with a unitary operator. We find that when the indefinite causal order of channels act on one-half of the entangled pair, then the shared state looses entanglement, but can retain non-zero quantum discord. This finding may have some interesting applications on its own where discord can be consumed as a resource. Our results suggest that the indefinite causal order along with a tiny amount of quantum discord can act as a resource in creating non-zero quantum coherence in the absence of entanglement.Comment: 9 pages, 4 figures, Accepted in Quantum Information Processin

Simultaneous Titrimetric Determination of La(lII) & Ce(IV) in Their Mixtures

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Self-consistent mode-coupling theory for the viscosity of rod-like polyelectrolyte solutions

A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rod-like polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-H\"{u}ckel approximation is inadequate even at low concentrations. The theory predicts a non-monotonic dependence of the reduced excess viscosity, $\eta_R$, on concentration from the behaviour of the static structure factor in polyelectrolyte solutions. The theory predicts that the peak in $\eta_R$ occurs at concentrations slightly lower than the overlap threshold concentration, $c^\ast$. The peak height increases dramatically with increasing molecular weight and decreases with increased concentrations of added salt. The position of the peak, as a function of concentration divided by $c^\ast$ is independent of salt concentration or molecular weight. The predictions can be tested experimentally.Comment: 9 pages, 9 figures (2 figures added in the revise version

Conserved Correlation in PT -symmetric Systems: Scattering and Bound States

For one-dimensional PT -symmetric systems, it is observed that the non-local product obtained from the continuity equation can be interpreted as a conserved corre- lation function. This leads to physical conclusions, regarding both discrete and continuum states of such systems. Asymptotic states are shown to have necessarily broken PT -symmetry, leading to modified scattering and transfer matrices. This yields restricted boundary conditions, e.g., in- cidence from both sides, analogous to that of the proposed PT CPA laser. The interpretation of left and right states leads to a Hermitian S-matrix, resulting in the non-conservation of the flux. This further satisfies a duality condition, identical to the optical analogues. However, the non-local conserved scalar implements alternate boundary conditions in terms of in and out states, leading to the pseudo-Hermiticity condition in terms of the scattering matrix. Interestingly, when PT -symmetry is preserved, it leads to stationary states with real energy, naturally inter- pretable as bound states. The broken PT -symmetric phase is also captured by this correlation, with complex-conjugate pair of energies, interpreted as resonances.Comment: 9 page

High Precision Measurements of Interstellar Dispersion Measure with the upgraded GMRT

Pulsar radio emission undergoes dispersion due to the presence of free electrons in the interstellar medium (ISM). The dispersive delay in the arrival time of pulsar signal changes over time due to the varying ISM electron column density along the line of sight. Correcting for this delay accurately is crucial for the detection of nanohertz gravitational waves using Pulsar Timing Arrays. In this work, we present in-band and inter-band DM estimates of four pulsars observed with uGMRT over the timescale of a year using two different template alignment methods. The DMs obtained using both these methods show only subtle differences for PSR 1713+0747 and J1909$-$3744. A considerable offset is seen in the DM of PSR J1939+2134 and J2145$-$0750 between the two methods. This could be due to the presence of scattering in the former and profile evolution in the latter. We find that both methods are useful but could have a systematic offset between the DMs obtained. Irrespective of the template alignment methods followed, the precision on the DMs obtained is about $10^{-3}$ pc cm$^{-3}$ using only BAND3 and $10^{-4}$ pc cm$^{-3}$ after combining data from BAND3 and BAND5 of the uGMRT. In a particular result, we have detected a DM excess of about $5\times10^{-3}$ pc cm$^{-3}$ on 24 February 2019 for PSR J2145$-$0750. This excess appears to be due to the interaction region created by fast solar wind from a coronal hole and a coronal mass ejection (CME) observed from the Sun on that epoch. A detailed analysis of this interesting event is presented.Comment: 11 pages, 6 figures, 2 tables. Accepted by A&