arXiv subjects
Publications and source records attributed to Mazhar Ali.
We construct a family of positive but not completely positive linear maps acting on four dimensional space. We employ these maps to detect bound entanglement in high dimensional quantum systems.
We have reexamined the moments of positive maps and the criterion based on these moments to detect entanglement. For two qubits, we observed that reduction map is equivalent to partial transpose map as the resulting matrices have the same set of eigenvalues although both matrices look different in same computational basis. Consequently, the detection power of both maps is same. For $2 \otimes 4$ systems, we find that moments of reduction map are capable to detect a family of bound entangled states. For qutrit-qutrit systems, we show that moments of reduction map can detect two well known families of bound entangled states. The moments of another positive map can detect the complete range of entanglement for a specific family of quantum states, whereas the earlier criterion fails to detect a small range of entangled states. For three qubits system, we find that applying reduction map to one of the qubit is equivalent to partial transpose operation. In particularly, for GHZ state and W state mixed with white noise, all the moments of a reduction map are exactly the same as the moments of partial transpose map.
We investigate entanglement dynamics of bipartite as well multipartite systems beyond Markov approximation. We study two pairs of cavity-reservoir systems, modeled as four qubits and track the change of entanglement among cavity-cavity qubits, reservoir-reservoir qubits, and also for genuine entanglement of all four qubits. For cavity-cavity qubits, we find that non-Markovianity prolongs the life of entanglement besides collapse/revival phenomenon. For reservoir-reservoir qubits, entanglement sudden birth is delayed accordingly along with oscillations. For all four qubits, with a specific initial state, we find that genuine entanglement develops gradually, reaches to a maximum constant value and then freezes at this value for some time before decaying. This sudden change in dynamics of genuine entanglement occurs for a time window where neither cavities nor reservoirs are entangled. In contrast to Markov process, sudden change phenomenon may be recurrent in non-Markovian regime.
We study genuine entanglement among $3$-qubits undergoing through a noisy process including dissipation, squeezing and decoherence. We obtain a general solution and analyze the asymptotic quantum states. It turns out that most of these asymptotic states can be genuinely entangled depending upon parameters of channel, memory parameter, and parameters of initial states. We study Greenberger-Horne-Zeilinger (GHZ) states and W states, mixed with white noise and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with bi-separable state (with specific mixture of white noise as described below) and end up with genuine entangled states. However, the memory parameter $\mu$ must be very high. We find that in contrast to two-qubit case, all three qubit asymptotic states for $n \to \infty$ are not genuinely entangled.
Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for $GHZ$ and $W$ states mixed with white noise.
The Heusler compounds have provided a playground of material candidates for various technological applications based on their highly diverse and tunable properties, controlled by chemical composition and crystal structure. However, physical exploration of the Heusler chemical space en masse is impossible in practice, hindering the exploration of the chemical composition vs. proprieties relationship. Many of these applications are related to the Heuslers electron transport characteristics, which are embedded in their electronic band structure (EBS). Here we we created a Heuslers dataset using the Materials Project (MP) database -- retrieving both chemical composition and their EBSs. We then used machine learning to develop a model correlating the composition vs. number of Dirac points in the EBS for Heuslers and also other Cubic compounds by identifying said Dirac points using an automated algorithm as well as generating chemical composition and global crystal structure features. Our ML model captures the overall trend, as well as identifies significant electronic and global crystal structure features, however, the ML model suffered from significant variance due to the lack of site specific features. Future work on a methodology for handling atomic site specific features will allow ML models to better match the underlying quantum mechanics governing the properties (also based on site specific properties) and capture the electronic properties in a more generalized approach.
Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment is directly connected to the robustness of the operating condition and is evaluated by analyzing proximity to the power flow solution space's boundary. Calculating location of such a boundary is a computationally challenging task, linked to the power flow equations' non-linear nature, presence of technological constraints, and complicated network topology. In this paper we introduce a general framework to characterize points on the power flow solution space boundary in terms of auxiliary variables subject to algebraic constraints. Then we develop an adaptive continuation algorithm to trace 1-dimensional sections of boundary curves which exhibits robust performance and computational tractability. Implementation of the algorithm is described in detail, and its performance is validated on different test networks.
It has been suggested that certain antiferromagnetic topological insulators contain axion quasiparticles (AQs), and that such materials could be used to detect axion dark matter (DM). The AQ is a longitudinal antiferromagnetic spin fluctuation coupled to the electromagnetic Chern-Simons term, which, in the presence of an applied magnetic field, leads to mass mixing between the AQ and the electric field. The electromagnetic boundary conditions and transmission and reflection coefficients are computed. A model for including losses into this system is presented, and the resulting linewidth is computed. It is shown how transmission spectroscopy can be used to measure the resonant frequencies and damping coefficients of the material, and demonstrate conclusively the existence of the AQ. The dispersion relation and boundary conditions permit resonant conversion of axion DM into THz photons in a material volume that is independent of the resonant frequency, which is tuneable via an applied magnetic field. A parameter study for axion DM detection is performed, computing boost amplitudes and bandwidths using realistic material properties including loss. The proposal could allow for detection of axion DM in the mass range between 1 and 10 meV using current and near future technology.
We study three independent pairs of Jaynes-Cummings systems such that two atoms might be correlated with each other but the third atom is uncorrelated with rest. We investigate the conditions under which these uncorrelated three atoms may become genuinely entangled. We find that this task is impossible if the cavity interacting with uncorrelated atom share classical correlations with any other cavity. We observe that atomic state can become genuine multipartite entangled, at least if the cavity with uncorrelated atom, is highly entangled with any other cavity. This is an interesting and non-trivial observation and may serve as another technique to generate multipartite entangled atoms via JC-interactions. The findings can be realized with available experimental setups.
Most studies of collective dephasing for bipartite as well as multipartite quantum systems focus on a very specific orientation of magnetic field, that is, z-orientation. However, in practical situations, there are always small fluctuations in stochastic field and it is necessary that more general orientations of fields should be considered. We extend this problem to qubit-qutrit systems and study correlation dynamics for entanglement and local quantum uncertainty for some specific quantum states. We find that certain quantum states exhibit freezing dynamics both for entanglement and local quantum uncertainty. We analyze the asymptotic states and find the conditions for having non-zero entanglement and local quantum uncertainty. Our results are relevant for ion-trap experiments and can be verified with current experimental setups.
We study dynamics of local quantum uncertainty (LQU) for a system of two cavities and two reservoirs. In the start, the cavities treated as two qubits are quantum correlated with each other, whereas reservoirs are neither correlated with each other nor with cavities. We answer two main questions in this work. First, how local quantum uncertainty decays from two quantum correlated cavities and grows among reservoirs. The second question is the examination of LQU developed among four qubits and also shed some light on its dynamics. We observe that LQU develops among reservoirs as kind of mirror image to its decay from cavities. For four qubits, we propose how to compute LQU such that the method is intuitive and conformable to the observation. We find that among four qubits LQU starts growing from zero to maximum value and then decays again to zero as the asymptotic state of cavities is completely transferred to reservoirs. We suggest the experimental setup to implement our results.
Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure over measurements. This measure is initially defined for bipartite quantum systems and a closed formula exists only for $2 \otimes d$ systems. We extend the idea of local quantum uncertainty to multi-qubit systems and provide the similar closed formula to compute this measure. We explicitly calculate local quantum uncertainty for various quantum states of three and four qubits, like GHZ state, W state, Dicke state, Cluster state, Singlet state, and Chi state all mixed with white noise. We compute this measure for some other well known three qubit quantum states as well. We show that for all such symmetric states, it is sufficient to apply measurements on any single qubit to compute this measure, whereas in general one has to apply measurements on all parties as local quantum uncertainties for each bipartition can be different for an arbitrary quantum state.
We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of {\it time-invariant} entanglement and {\it freezing} dynamics of entanglement for this dimension of Hilbert space. Interestingly, we find that for qubit-qutrit systems both of these peculiar features coexist, that is, we observe not only time-invariant entanglement for certain quantum states but we find also find evidence that many quantum states freeze their entanglement after decaying for some time. To our knowledge, the existance of both these phenomena for one dimension of Hilbert space is not found so far. All previous studies suggest that if there is freezing dynamics of entanglement, then there is no time-invariant entanglement and vice versa. In addition, we study local quantum uncertainity and other correlations for certain families of states and discuss the interesting dynamics. Our study is an extension of similar studies for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems.
We examine the possibilities of non-trivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for qutrit-qutrit quantum systems. We find no evidence for time-invariant entanglement, however, we do observe that quantum states freeze their entanglement after decaying for some time. It is interesting that quantum states are changing whereas their entanglement remains constant. We find that the combined action of decoherence free subspaces and subspaces where quantum states decay, facilitate this phenomenon. This study is an extension of similar phenomena observed for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems. We examine nonlocality of a specific family of states and find the certain instances where the states still remain entangled, however they can either loose their nonlocality at a finite time or remain nonlocal for all times.
Topological materials which possess topologically protected surface states have attracted much attention in recent years. In this work, we study the critical current of superconductor/inversion symmetry breaking topological material/superconductor junctions. We found surprisingly that, in topological materials with broken inversion symmetry, the magnitude of the critical Josephson currents $|I^{+}_c(B)|$ at fixed magnetic field $B$ is not the same for critical currents $|I^{-}_c(B)|$ flowing in the opposite direction. Moreover, the critical currents violate the $| I_{c}^{\pm}(B)| = |I_{c}^{\pm}(-B)|$ relation and give rise to asymmetric Fraunhofer patterns. We call this phenomenon asymmetric Josephson effect (AJE). AJE can be use to detect inversion symmetry breaking in topological materials such as in quantum spin Hall systems and Weyl semimetals.
Recent years have seen the rapid discovery of solids whose low-energy electrons have a massless, linear dispersion, such as Weyl, line-node, and Dirac semimetals. The remarkable optical properties predicted in these materials show their versatile potential for optoelectronic uses. However, little is known of their response in the picoseconds after absorbing a photon. Here we measure the ultrafast dynamics of four materials that share non-trivial band structure topology but that differ chemically, structurally, and in their low-energy band structures: ZrSiS, which hosts a Dirac line node and Dirac points; TaAs and NbP, which are Weyl semimetals; and Sr$_{1-y}$Mn$_{1-z}$Sb$_2$, in which Dirac fermions coexist with broken time-reversal symmetry. After photoexcitation by a short pulse, all four relax in two stages, first sub-picosecond, and then few-picosecond. Their rapid relaxation suggests that these and related materials may be suited for optical switches and fast infrared detectors. The complex change of refractive index shows that photoexcited carrier populations persist for a few picoseconds.
We study the dynamics of genuine multipartite entanglement for quantum systems upto four qubits interacting with general collective dephasing process. Using a computable entanglement monotone for multipartite systems, we observe the feature of freezing dynamics of genuine entanglement for three and four qubits entangled states. We compare the dynamics with that of random states and find that most states exibit this feature. We then study the effects of collective dephasing on genuine nonlocality and find out that although quantum states remain genuinely entangled yet their genuine nonlocality is lost in a finite time. We show the sensitivity of asymptotic states being genuinely entangled by mixing white noise.
We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We point out that quantum states exhibiting time-invariant entanglement must live in both decoherence free subspace and in the subspaces orthogonal to it. The previous studies on this feature for two qubits can be recovered from our studies as a special case. We also study the nonlocality of quantum states under collective dephasing. We find that although genuine entanglement of quantum states may not change, however their nonlocality changes. We discuss the possibility of finite time end of genuine nonlocality.