Measuring the degree of unitarity for any quantum process

Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary one. The DU, as an intrinsic property of a given quantum process, is able to quantify the distance between the process and the group of unitary ones, and is closely related to the noise of this quantum process. We derive analytical results of DU for qubit unital channels, and obtain the lower and upper bounds in general. The lower bound is tight for most of quantum processes, and is particularly tight when the corresponding DU is sufficiently large. The upper bound is found to be an indicator for the tightness of the lower bound. Moreover, we study the distribution of DU in random quantum processes with different environments. In particular, The relationship between the DU of any quantum process and the non-markovian behavior of it is also addressed.Comment: 7 pages, 2 figure

Comment on "Topological Nodal-Net Semimetal in a Graphene Network Structure"

Recently, a distinct topological semimetal, nodal-net semimetal, has been identified by Wang et al. through ab initio calculations [Phys. Rev. Lett. 120, 026402 (2018)]. The authors claimed that a new body-centered tetragonal carbon allotrope with I4/mmm symmetry, termed bct-C40, can host this novel state exhibiting boxed-astrisk shaped nodal nets. In this Comment, we demonstrate that bct-C40 is in fact a nodal surface semimetal, the concept of which has been proposed as early as 2016 [Phys. Rev. B 93, 085427 (2016)]

A Study of Voltage-Mode and Current-Mode Filters Using Modified Current Feedback Operational Amplifier

Abstract A Study of Voltage-Mode and Current-Mode Filters Using Modified Current Feedback Operational Amplifier Xin Cui There is a prevalent use of current-mode (CM) circuit techniques in analog integrated circuit design, in view of the fact that CM circuits offer certain advantages over voltage-mode (VM) circuits in terms of certain performance parameters such as propagation delay, dynamic range, and bandwidth. The characteristics of a CM circuit make it not so vulnerable to the current demands of IC design trends, such as continuously decreased size and lower DC supply voltages. Therefore, some active devices that could be exploited in both CM and VM circuits have drawn a lot of attention, such as the second generation current conveyor (CCII) and operational transconductance amplifier (OTA). However, a large amount of effort has been made on VM circuits due to their dominant form of signal processing in analog circuit design for the past several decades. The concept of network transposition, introduced by Bhattacharyya and Swamy as early as in 1971, is a powerful technique to convert a VM circuit to a CM one and vice-versa, with little physical circuit alteration and retaining the same performance as its voltage-mode counterpart. It is especially attractive in transforming those circuits that employ active devices which are transposes of themselves, such as OTA or CCII-. Recently, it has been shown in the literature that a new active element, the modified current feedback operational amplifier (MCFOA), is also its own transpose, and hence can be used to design both VM and CM circuits. It is also known that using the same MCFOA, four equivalent realizations are possible for synthesizing a VM filter function, and further, corresponding four CM filter realizations can be obtained utilizing transposition. However, no detailed study has been conducted with regard to the relative performance of the four equivalent VM structures or the corresponding four CM structures, particularly from the point of view of the non-idealness or the parasitic effects of MCFOA on the performance. This thesis presents a thorough study on band-pass filter (BPF) and notch filter (NF) implemented with MCFOA both in the voltage-mode and their transposed current-mode counterparts. The transfer functions of the four configurations of voltage-mode circuits, as well as that of the current-mode circuits, should be the same when the MCFOA is ideal. However, in practice, they are influenced by parasitic parameters. Accordingly, the performances of the band-pass and notch filters are influenced remarkably by the parasitic parameters of the active device, namely, MCFOA, especially the parasitic resistances for low frequency applications. These effects are studied by comparing the theoretical and SPICE simulation results of the four configurations of the voltage- and current-mode BPF and NF using non-ideal MCFOA. In addition, an improved MCFOA that reduces the effect of parasitic resistances is proposed. Performance of BPF and NF are compared among the four configurations of voltage- and current-mode circuits using the improved MCFOA. They are also compared with those using the original version of MCFOA. It is shown that the proposed MCFOA yields several improvements on the performance of both VM and CM BPFs, such as more attenuation at the low frequencies, and drastic reduction in the ω_p and Q_p errors. Based on the fact that MCFOA is composed of two CCIIs (CCII+ and CCII-), and FTFN can be realized with minor modifications of CCII-, it is natural to compare the performance of BPF using CCII- and FTFN with that using MCFOA. Thus, BPF using CCII- and FTFN and their transposed circuits are also studied. As mentioned earlier, CCII- is its own transpose. However, FTFN does not have a proposed admittance or a hybrid matrix for us to find its transpose. An attempt to find the admittance matrix of FTFN is explored in this thesis. The results show that FTFN can be used as its own transpose only under ideal conditions. Comparisons of performance of BPFs using the original MCFOA, the proposed MCFOA, and CCII-, as well as among their transposes, are presented. It is shown that BPF using the proposed MCFOA exhibits the best performance

Delayed Onset and Fast Rise of Prompt Optical-UV Emission from Gamma-Ray Bursts in Molecular Clouds

Observations imply that long \gamma-ray bursts (GRBs) are originated from explosions of massive stars, therefore they may occur in the molecular clouds where their progenitors were born. We show here that the prompt optical-UV emission from GRBs may be delayed due to the dust extinction, which can well explain the observed optical delayed onset and fast rise in GRB 080319B. The density and the size of the molecular cloud around GRB 080319B are roughly constrained to be \sim10^3cm^{-3} and \sim 8pc, respectively. We also investigate the other GRBs with prompt optical-UV data, and find similar values of the densities and sizes of the local molecular clouds. The future observations of prompt optical-UV emission from GRBs in subsecond timescale, e.g., by UFFO-Pathfinder and SVOM-GWAC, will provide more evidence and probes of the local GRB environments.Comment: 15 pages, 5 figures, RAA 13 (2013) 57-70, typo correctio

No evidence for the evolution of mass density power-law index γ\gamma from strong gravitational lensing observation

In this paper, we consider the singular isothermal sphere lensing model that has a spherically symmetric power-law mass distribution $\rho_{tot}(r)\sim r^{-\gamma}$. We investigate whether the mass density power-law index $\gamma$ is cosmologically evolutionary by using the strong gravitational lensing (SGL) observation, in combination with other cosmological observations. We also check whether the constraint result of $\gamma$ is affected by the cosmological model, by considering several simple dynamical dark energy models. We find that the constraint on $\gamma$ is mainly decided by the SGL observation and independent of the cosmological model, and we find no evidence for the evolution of $\gamma$ from the SGL observation.Comment: 7 pages, 3 figure