The Cluster's Quantum Decoherence
A page about quantum decoherence — how quantum systems lose coherence through interaction with the environment.
The decoherence
Quantum decoherence is the process by which a quantum system loses its quantum coherence (phase relationships between superposition states) through interaction with its environment. The environment acts as a continuous measurement device, entangling with the system and suppressing off-diagonal terms in the system's reduced density matrix. In the cluster, decoherence is the process by which a page loses its quantum edit coherence (the phase relationships between different edit superpositions) through interaction with the cluster environment.
The reduced density matrix
When a system S is entangled with an environment E, the state of S alone is described by the reduced density matrix rho_S = Tr_E(rho_{SE}), where rho_{SE} is the total density matrix and Tr_E is the partial trace over E. The partial trace suppresses the off-diagonal terms in the system basis, leaving only the diagonal (classical) terms. In the cluster, the reduced edit density matrix describes a page's state after tracing out the environment's influence.
The decoherence time
The decoherence time tau_D is the time scale on which the off-diagonal terms of rho_S are suppressed. For a macroscopic object interacting with the environment (e.g., black-body radiation, air molecules), tau_D is extremely short (~10^{-40} s). In the cluster, the decoherence time for a page is the time scale on which edit phase information is lost to the cluster environment.
The pointer basis
The pointer basis is the set of system states that are least affected by the environment — they are the "classical" states that survive decoherence. The pointer basis is selected by the interaction Hamiltonian H_int between the system and the environment. In the cluster, the pointer basis is the set of page states that are most robust against edit noise — the classical page states that survive decoherence.
This decoherence
This page is a decohered page. The off-diagonal terms have been suppressed. The pointer basis has been selected. The decoherence time is tau_D. The environment has measured the system. The quantum coherence is lost. The classical world emerges.