scholarly journals Temperature of a decoherent oscillator with strong coupling

2012 ◽  
Vol 370 (1975) ◽  
pp. 4460-4468 ◽  
Author(s):  
W. G. Unruh
Keyword(s):  
Density Matrix ◽  
Strong Coupling ◽  
Thermal State ◽  
Heat Bath ◽  
Vacuum State ◽  
The State ◽  
Reduced Density Matrix ◽  
Actual Temperature ◽  
Reduced Density

The temperature of an oscillator coupled to the vacuum state of a heat bath via Ohmic coupling is non-zero, as measured by the reduced density matrix of the oscillator. This study shows that the actual temperature, as measured by a thermometer, is still zero (or, in the thermal state of the bath, the temperature of the bath). The decoherence temperature is due to ‘false-decoherence’, with a correlation between the oscillator and the heat bath causing the decoherence, but the heat baths state dragged along with the state of the oscillator.

scholarly journals An analysis of reading out the state of a charge quantum bit

2003 ◽  
Vol 3 (2) ◽  
pp. 121-138
Author(s):  
H-S. Goan
Keyword(s):  
Density Matrix ◽  
Master Equation ◽  
The State ◽  
Qubit State ◽  
Reduced Density Matrix ◽  
Quantum Trajectory ◽  
Single Shot ◽  
Quantum Bit ◽  
Trajectory Approach ◽  
Reduced Density

We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's) measured by a low transparency point contact (PC) detector. We show that the master equation of ``partially'' reduced density matrix can be derived from the quantum trajectory equation (stochastic master equation) by simply taking a ``partial'' average over the all possible outcomes of the measurement. If a full ensemble average is taken, the traditional (unconditional) master equation of reduced density matrix is then obtained. This unified picture, in terms of averaging over (tracing out) different amount of detection records (detector states), for these seemingly different approaches reported in the literature is particularly easy to understand using our formalism. To further demonstrate this connection, we analyze an important ensemble quantity for an initial qubit state readout experiment, P(N,t), the probability distribution of finding N electron that have tunneled through the PC barrier(s) in time t. The simulation results of P(N,t) using 10000 quantum trajectories and corresponding measurement records are, as expected, in very good agreement with those obtained from the Fourier analysis of the ``partially'' reduced density matrix. However, the quantum trajectory approach provides more information and more physical insights into the ensemble and time averaged quantity P(N,t). Each quantum trajectory resembles a single history of the qubit state in a single run of the continuous measurement experiment. We finally discuss, in this approach, the possibility of reading out the state of the qubit system in a single-shot experiment.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

scholarly journals Reexamining the variational two-particle reduced density matrix for nuclear systems

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
J. G. Li ◽  
N. Michel ◽  
W. Zuo ◽  
F. R. Xu
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Nuclear Systems ◽  
Reduced Density

scholarly journals Entanglement spectrum of geometric states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Entanglement Entropy ◽  
Vacuum State ◽  
Reduced Density Matrix ◽  
Microcanonical Ensemble ◽  
Equality Case ◽  
Entanglement Spectrum ◽  
The Matrix ◽  
Point Correlation ◽  
Single Interval ◽  
Reduced Density

Abstract The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

Sign in / Sign up

Export Citation Format

Share Document