Dynamics of a Quantum Reference Frame

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles

The Absolute Frame of Reference

The manuscript found the formula to calculate the real velocity of the earth and the maximum velocity in the universe, the values of the quantities after calculation as follows: V_earth = 1.852819296∗10^8 m/s.-- C_max = 4.8507438399∗10^8 m/s.-- In order to calculate the above results, the manuscript has built a reference frame transformation suitable for all types of motion(suitable for both linear motion and chaotic motion of the reference frame). This means that we will calculate the velocity of an object without using the distance S quantity of the object

Microarcsecond instability of the celestial reference frame

The fluctuation of the angular positions of reference extragalactic radio and optical sources under the influence of the irregular gravitational field of visible Galactic stars is considered. It is shown that these angular fluctuations range from a few up to hundreds of microarcseconds. This leads to a small rotation of the celestial reference frame. The nondiagonal coefficients of the rotation matrix are of the order of a microarcsecond. The temporal variation of these coefficients due to the proper motion of the foreground stars is of the order of one microsecond per 20 years. Therefore, the celestial reference frame can be considered inertial and homogeneous only to microarcsecond accuracy. Astrometric catalogues with microarcsecond accuracy will be unstable, and must be reestablished every 20 years.Comment: 5 pages, 2 figures, accepted to MNRA

Quantum communication using a bounded-size quantum reference frame

Typical quantum communication schemes are such that to achieve perfect decoding the receiver must share a reference frame with the sender. Indeed, if the receiver only possesses a bounded-size quantum token of the sender's reference frame, then the decoding is imperfect, and we can describe this effect as a noisy quantum channel. We seek here to characterize the performance of such schemes, or equivalently, to determine the effective decoherence induced by having a bounded-size reference frame. We assume that the token is prepared in a special state that has particularly nice group-theoretic properties and that is near-optimal for transmitting information about the sender's frame. We present a decoding operation, which can be proven to be near-optimal in this case, and we demonstrate that there are two distinct ways of implementing it (corresponding to two distinct Kraus decompositions). In one, the receiver measures the orientation of the reference frame token and reorients the system appropriately. In the other, the receiver extracts the encoded information from the virtual subsystems that describe the relational degrees of freedom of the system and token. Finally, we provide explicit characterizations of these decoding schemes when the system is a single qubit and for three standard kinds of reference frame: a phase reference, a Cartesian frame (representing an orthogonal triad of spatial directions), and a reference direction (representing a single spatial direction).Comment: 17 pages, 1 figure, comments welcome; v2 published versio

Sampled Reference Frame Algorithm Based on Space Vector Pulse Width Modulation for Five Level Cascaded H-Bridge Inverter

In This paper the Sampled Reference Frame Algorithm for Five Level Cascaded H-Bridge Inverter is presented. This simple method is less computation method than Sector Identification. This SVPWM can drive any Multilevel Inverter with good DC utilization, less switching stress. This is used for high voltage and high power applications. By using Sampled Reference Frame Algorithm, there is no use of look up tables, sector selection, no need of reference voltage and angle information, 3φ to 2φ transformation. The inverter's structure of these inverters is developed by using MATLAB SIMULINK software