Pauli Quantum Research Articles

A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries

Abstract A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps have already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing intricate relation between positivity, operator Schwarz inequality, and complete positivity. Finally, it is shown how to generalize the entire picture beyond unital case (so called generalized Schwarz maps). Interestingly, the first example of Schwarz but not completely positive map found by Choi belongs to our class. As a case study we provide a full characterization of Pauli maps. Our analysis leads to generalization of seminal Fujiwara–Algoet conditions for Pauli quantum channels.

Realization of Tristate Pauli-X, Y and Z gates on photonic crystal using wavelength encoding

Pauli gates using phase encoding technique are well-known in quantum optical computing. In this paper, all-optical Tristate Pauli quantum gates are designed by using the wavelength encoding technique. In addition to this, four Y-gates, two Z-gates and one from each gate are integrated separately. Then the Pauli-X gate, integrated Pauli-Y gate, integrated Pauli-Z gate and integrated Pauli-X, Y and Z gate are designed on Photonic crystal-based layouts which improve the bit rate and response time significantly. Simulation results are realized by finite difference time domain (FDTD) method.The states of signals are identified by their wavelengths which eliminates the troublesome of maintaining the specific phases or polarization of states. Here, the simulation results prove the feasibility of the operations. The designing of all-optical logic systems on photonic crystal makes these suitable for ultrafast quantum computing.

Quantum state preparation and one qubit logic from third-order nonlinear interactions

We present a study on preparing and manipulating temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the x y plane, allowing spanning the full Bloch sphere in two steps. Particularly, we present a method to obtain any of the Pauli quantum gates by varying geometric or user-accessible parameters in a given experimental configuration when time-ordering effects are ignored. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.

Error Thresholds for Arbitrary Pauli Noise

The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code for noise modeled by that channel. Discretizing the single-qubit errors leads to the important family of Pauli quantum channels; curiously, multipartite entangled states can increase the threshold of these channels beyond the so-called hashing bound, an effect termed superadditivity of coherent information. In this work, we divide the simplex of Pauli channels into one-parameter families and compute numerical lower bounds on their error thresholds. We find substantial increases of error thresholds relative to the hashing bound for large regions in the Pauli simplex corresponding to biased noise, which is a realistic noise model in promising quantum computing architectures. The error thresholds are computed on the family of graph states, a special type of stabilizer state. In order to determine the coherent information of a graph state, we devise an algorithm that exploits the symmetries of the underlying graph, resulting in a substantial computational speed-up. This algorithm uses tools from computational group theory and allows us to consider symmetric graph states on a large number of vertices. Our algorithm works particularly well for repetition codes and concatenated repetition codes (or cat codes), for which our results provide the first comprehensive study of superadditivity for arbitrary Pauli channels. In addition, we identify a novel family of quantum codes based on tree graphs. The error thresholds of these tree graph states outperform repetition and cat codes in large regions of the Pauli simplex, and hence form a new code family with desirable error correction properties.

Optical holonomic single quantum gates with a geometric spin under a zero field

Realization of fast fault-tolerant quantum gates on a single spin is the core requirement for solid-state quantum-information processing. As polarized light shows geometric interference, spin coherence is also geometrically controlled with light via the spin-orbit interaction. Here, we show that a geometric spin in a degenerate subspace of a spin-1 electronic system under a zero field in a nitrogen vacancy center in diamond allows implementation of optical non-adiabatic holonomic quantum gates. The geometric spin under quasi-resonant light exposure undergoes a cyclic evolution in the spin-orbit space, and acquires a geometric phase or holonomy that results in rotations about an arbitrary axis by any angle defined by the light polarization and detuning. This enables universal holonomic quantum gates with a single operation. We demonstrate a complete set of Pauli quantum gates using the geometric spin preparation and readout techniques. The new scheme opens a path to holonomic quantum computers and repeaters.

Dispersive and dissipative nonlinear structures in degenerate Fermi–Dirac Pauli quantum plasma

We study the interplay between dispersion due to the electron degeneracy parameter and dissipation caused by plasma resistivity, in degenerate Fermi–Dirac Pauli quantum plasma. Considering relativistic degeneracy pressure for electrons, we investigate both arbitrary and small amplitude nonlinear structures. The corresponding trajectories are also plotted in the phase plane. The linear analysis for the dispersion relation yields interesting features. The present work is anticipated to be of physical relevance in the study of compact magnetized astrophysical objects like white dwarfs.

Canonical Naimark extension for generalized measurements involving sets of Pauli quantum observables chosen at random

We address measurement schemes where certain observables are chosen at random within a set of non-degenerate isospectral observables and then measured on repeated preparations of a physical system. Each observable has a given probability to be measured, and the statistics of this generalized measurement is described by a positive operator-valued measure (POVM). This kind of schemes are referred to as quantum roulettes since each observable is chosen at random, e.g. according to the fluctuating value of an external parameter. Here we focus on quantum roulettes for qubits involving the measurements of Pauli matrices and we explicitly evaluate their canonical Naimark extensions, i.e. their implementation as indirect measurements involving an interaction scheme with a probe system. We thus provide a concrete model to realize the roulette without destroying the signal state, which can be measured again after the measurement, or can be transmitted. Finally, we apply our results to the description of Stern-Gerlach-like experiments on a two-level system.

PATH INTEGRAL AND PSEUDOCLASSICAL ACTION FOR SPINNING PARTICLE IN EXTERNAL ELECTROMAGNETIC AND TORSION FIELDS

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a pseudoclassical action for a spinning particle. It is just a generalization of Berezin–Marinov action to the background under consideration. Pseudoclassical equations of motion in the nonrelativistic limit reproduce exactly the classical limit of the Pauli quantum mechanics in the same case. Quantization of the action appears to be nontrivial due to an ordering problem, which needs to be solved to construct operators of first-class constraints, and to select the physical sector. Finally the quantization reproduces the Dirac equation in the given background and, thus, justifies the interpretation of the action.

On the approach to statistical equilibrium of a quantum macrosystem

Solving the Pauli quantum master equation by means of a method proposed by van Kampen and recently developed by Tomita and Tomita, we give a quantitative description of the evolution to wards the equilibrium state of a quantum macrosystem and of the fluctuations around the mean values of its energy. The probability distribution of these fluctuations turns out to be of a Gaussian shape with a variance function of time and approaching, fort→∞, a constant value. Finally an application is made to the phenomenon of spin relaxation.

The Electric Moment of Gaseous Molecules of Halogen Hydrides

Dielectric constant of the hydrogen halides HCl, HBr and HI to 300\ifmmode^\circ\else\textdegree\fi{}C.---An improved heterodyne null method of measurement was used in which the beats between two high frequency oscillations from separate electron tube generators are adjusted to the frequency of a tuning fork, the small change of capacity due to the introduction of the gas being compensated by a large change in a large capacity in series with the gas condenser. Measurements were made at atmospheric pressure, using carefully purified gases, over a range of nearly 400\ifmmode^\circ\else\textdegree\fi{} from just above the liquefaction point. The results are well represented by the Debye equation $(\ensuremath{\epsilon}\ensuremath{-}1)vT=AT+B$, where $v$ is the specific volume and $T$ the absolute temperature. [The values found for $A$ are.001040 (HCl),.001212 (HBr) and.001856 (HI); and for $B$ are.895(HCl),.52(HBr) and.12(HI)]. This agreement lends support to the Debye classical theory of electric polarization due to fixed moments in the molecule. The values obtained for the electric moment of the molecules are, in ${10}^{\ensuremath{-}18}$ c.g.s.u., 1.034(HCl), 0.79(HBr) and 0.38(HI). The Pauli quantum theory gives an equation of the same form as Debye's but leads to smaller values for the electric moment. The upper limit for the moment given by infra-red absorption data for HCl, however, is 6 times the classical value and 13 times the quantum value and hence does not decide between the two theories.Dielectric constant for hydrogen, oxygen, nitrogen and air.---The values obtained for $(\ensuremath{\epsilon}\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ at 0\ifmmode^\circ\else\textdegree\fi{}C and 760 mm pressure are 265, 518, 581 and 572 for ${\mathrm{H}}_{2}$, ${\mathrm{O}}_{2}$, ${\mathrm{N}}_{2}$ and air, accurate probably to within 1/2 per cent.