Advantages Of Density Matrices

Density Matrices:

“The density matrix or density operator is an alternate representation of the state of a quantum system for which we have previously used the wave-function. Although describing a quantum system with the density matrix is equivalent to using the wave-function, one gains significant practical advantages using the density matrix for certain time-dependent problems – particularly relaxation and nonlinear spectroscopy in the condensed phase. The density matrix is formally defined as the outer product of the wave-function and its conjugate.”

- 5.74 Introduction to Quantum Mechanics II, MIT Open Courseware (Spring 2009) A reduced density matrix can be seen as some form of solution to the infamous measurement problem of quantum mechanics

.This scattering-induced decoherence is ubiquitous in nature and of paramount importance in describing the quantum-to-classical transition on macroscopic everyday-world scales.

APPROACHES TO QUANTUM DECOHERENCE So far we have laid the framework and the fundamental science needed to understand the concept of decoherence. It’s a field which transpires many questions on the upfront and covers angles from the deep philosophical arguments of localism and realism to the tech-savvy modern engineering.

Bacciagaluppi (2003) mentions, “Decoherence is relevant (or is claimed to be relevant) to a variety of questions ranging from the measurement problem to the arrow of time, and in particular to the question of whether and how the ‘classical world’ may emerge from quantum mechanics.”

To see quantum mechanical behavior, a system must separate into two different states and then be brought back together. Describing this as a process: Start in a state, split that state into two components (a coherent superposition), and bring the states back

If the two parts of the quantum wave function interact with the rest of the Universe while they were apart, they change the Universe. If this happens, then when you try to bring the states back together, the Universe has changed (and you can't un-change the Universe simply, it's like unscrambling an egg).

Schlosshauer in his 2003 research paper asserts that, “The decoherence program is based on the idea that such quantum correlations are ubiquitous; that nearly every physical system must interact in some way with its environment (for example, with the surrounding photons that then create the visual experience within the observer), which typically consists of a large number of degrees of freedom that are hardly ever fully controlled. Only in very special cases of typically microscopic (atomic) phenomena, so goes the claim of the decoherence program, is the idealization of isolated systems applicable so that the predictions of linear quantum mechanics (i.e., a large class of super-positions of states) can actually be observationally