quantumcoherence

Quantum coherence is the property of a quantum system to preserve definite phase relationships between its constituent states. Coherence enables interference and underpins quantum superposition, allowing a system to behave as if its components are in a single, well-defined phase relationship.

In formal terms, coherence is carried by the off-diagonal elements of the system’s density matrix in a chosen basis. For a pure state, the state vector encodes a definite relative phase; for a mixed state, diminished or absent off-diagonal terms indicate loss of coherence. Coherence can be discussed in terms of temporal or spatial aspects and across internal degrees of freedom such as spin, energy levels, or photonic modes.

Coherence manifests in settings such as the temporal coherence of light and the spatial coherence of extended objects, as well as in internal quantum degrees of freedom like spins or energy levels in atoms, ions, photons, or superconducting qubits. Its persistence is characterized by a coherence time or a coherence length, depending on the system and measurement.

Decoherence occurs when the system interacts with its environment, causing the off-diagonal terms to decay and classical probabilities to emerge. Dephasing time (T2) and relaxation time (T1) describe these processes, often modeled with environmental fluctuations via quantum channels or Markovian baths.

Experimentally, coherence is inferred from interference visibility, fringe contrast, or spectral linewidths. While coherence is necessary for entanglement, it is not equivalent to it; a system can be coherent without being entangled with other degrees of freedom.

Quantum coherence is central to quantum information processing, metrology, and imaging, enabling phase-sensitive measurements, quantum gates, and wave-like dynamics that enhance performance in various technologies. It also influences transport and reaction dynamics in condensed matter and chemistry.