Decoherence

# tag · @ author · ! scientist

Decoherence is the process by which a quantum system loses its interference properties and begins to behave according to classical physics. This happens because the system inevitably becomes entangled with countless environmental particles. The information about the superposition is 'smeared' into the environment, and quantum alternatives become indistinguishable. It is decoherence that resolves the famous Schrödinger's cat paradox: a macroscopic object cannot remain in a superposition of alive-dead for long due to the rapid destruction of coherence.

History

The concept was formulated in the 1970s–80s by H. Dieter Zeh and Wojciech Zurek, although its roots go back to John von Neumann's analysis of measurement in quantum mechanics.

How it works

Imagine a pure musical note in a silent hall. If you sing on a busy street, the voice mixes with noise, and it becomes impossible to extract the original note. Similarly, quantum coherence is 'blurred' due to the chaotic influence of the environment.

💡 Decoherence acts rapidly: for a dust-sized object, a superposition of two positions is destroyed in about 10⁻³¹ seconds due to interaction with the cosmic background.

Quantum decoherence is the irreversible loss of phase coherence between the components of a superposition due to the entanglement of the system with the environment. The environment acts as a continuous measuring device, fixing the system in a particular basis (einselection). Mathematically, it is described by the Caldeira-Leggett model or the Lindblad equation for the density matrix. The off-diagonal elements of the density matrix decay exponentially, with the decoherence time inversely proportional to the square of the distance between states and the interaction strength. Although the evolution of the whole system (object + environment) remains unitary, an effective loss of quantumness occurs for the subsystem. Decoherence underlies the quantum-to-classical transition and modern interpretations of quantum mechanics.

History

The foundation was laid by von Neumann's analysis of quantum measurement (1932). In 1970, H. Dieter Zeh realized the role of the environment in a conversation with Erich Joos. Wojciech Zurek formalized the theory in the 1980s–1990s, introducing einselection and quantum Darwinism. Experimental confirmations were obtained in atom interferometry and superconducting qubits. David Deutsch emphasized the importance of decoherence for quantum computing.

How it works

The initial superposition |ψ⟩ = α|0⟩ + β|1⟩ with the environment in state |E₀⟩ evolves after interaction into an entangled state: α|0⟩|E₀⟩ + β|1⟩|E₁⟩. If the environment states |E₀⟩ and |E₁⟩ are orthogonal, interference vanishes, and the reduced density matrix of the system becomes diagonal: ρ = |α|²|0⟩⟨0| + |β|²|1⟩⟨1|. The decoherence time is estimated as t_D ~ 1/(γ d²), where γ is the interaction constant, d is the separation of states. Combating decoherence is the main challenge in creating quantum computers, solved with error-correcting codes.

\frac{d\rho}{dt} = -\frac{i}{\hbar}[H,\rho] + \sum_k \left( L_k \rho L_k^\dagger - \frac{1}{2}\{L_k^\dagger L_k, \rho\} \right)

ρ — density matrix of the system, H — Hamiltonian, ℏ — reduced Planck constant (≈ 1.05×10⁻³⁴ J·s), L_k — Lindblad operators (describe decoherence and dissipation), [·,·] — commutator, {·,·} — anticommutator

Open problems & fun facts

Suppression of decoherence in qubits for scalable quantum processors; Understanding the boundary between the quantum and classical worlds with multiple observers; Observation of decoherence in increasingly macroscopic objects

💡 In superconducting qubits, coherence times reach hundreds of microseconds, allowing thousands of quantum operations before information loss.

No articles yet

Decoherence

History

How it works

History

How it works

History

How it works

Open problems & fun facts

Related articles