The term decoherence is derived from the prefix de- (from Latin), meaning “down, away, or reversal,” and the root coherence, which originates from the Latin verb cohaerēre:
• De-: Suggests separation, loss, or reversal.
• Coherence: Comes from the Latin co- (together) and haerēre (to stick or cling). In English, coherence refers to the quality of being logical, consistent, or unified.
When combined, decoherence literally means the process of losing coherence or unity. The term was first introduced in its technical sense within quantum mechanics in the 20th century to describe the loss of quantum phase relationships, leading to classical-like behaviour. It has since been extended metaphorically into other fields like psychology and philosophy.
Abstract
Decoherence is the process by which quantum systems lose coherence, transitioning from quantum superpositions to classical statistical mixtures. This phenomenon is central to explaining the emergence of classicality in quantum systems without invoking wavefunction collapse. This paper explores decoherence as coherence decay, providing precise definitions, mathematical formulations, and an analysis of the underlying physical mechanisms. The discussion focuses on the dynamics of coherence loss and its implications for the quantum-to-classical transition, supported by a rigorous theoretical framework and references to foundational and contemporary literature.
1. Introduction
The transition from quantum to classical behaviour is a fundamental question in physics, addressed in part by the phenomenon of decoherence. In its simplest terms, decoherence refers to the loss of quantum coherence in a system due to interactions with its surrounding environment. As a result of this process, phase relationships between the components of a quantum superposition state decay, giving rise to classical-like behaviour.
Understanding decoherence is crucial for several reasons. It clarifies the quantum-to-classical transition, provides insights into the role of measurement in quantum mechanics, and establishes limitations for quantum technologies such as quantum computing. This paper focuses on decoherence as coherence decay, analysing its mechanisms, mathematical descriptions, and its role in the emergence of classical physics.
2. Coherence in Quantum Mechanics
2.1. Defining Coherence
Coherence in quantum mechanics is the preservation of well-defined phase relationships between different components of a quantum state.
Quantum coherence is a prerequisite for interference and entanglement, distinguishing quantum systems from classical ones. It allows systems to exist in superposition states and exhibit interference effects, as seen in iconic experiments like the double-slit experiment.
3. Decoherence as Coherence Decay
3.1. Definition of Decoherence
Decoherence is the process by which the off-diagonal elements of the density matrix decay over time due to interactions with the environment. This decay signifies the loss of quantum phase relationships, which erases interference effects and transitions the system toward classical behaviour. Importantly, decoherence does not imply the collapse of the wavefunction but rather the apparent emergence of classicality when a quantum system is viewed as part of an open system.
Zurek (2003) described decoherence as a “dynamical suppression of interference” caused by the system’s coupling with environmental degrees of freedom, such as photons, phonons, or molecular vibrations.
3.2. Mathematical Framework
The reduced density matrix for a system interacting with an environment is obtained by tracing out the environmental degrees of freedom:
Psystem = Trenv (Psystem + env)
Through this process, the off-diagonal elements of Psystem decay, leading to the suppression of quantum coherence:
where rij (Gamma ij) represents the decoherence rate, which depends on the strength of the system-environment coupling and the properties of the environment.
This decay of coherence results in the suppression of interference effects, leaving a diagonal density matrix that resembles a classical statistical mixture.
3.3. Mechanisms of Coherence Decay
3.3.1. Interaction with the Environment
Decoherence occurs when a quantum system becomes entangled with its environment. The environment effectively “measures” the quantum system by interacting with it, transferring phase information into its own degrees of freedom. These interactions can be caused by:
• Photonic scattering: Interaction with ambient photons, which carry away phase information.
• Thermal fluctuations: Coupling with a thermal reservoir, leading to random phase shifts.
• Atomic collisions: Interaction with surrounding particles in a gas or liquid.
The information about the quantum system becomes encoded in the environment, rendering the coherence inaccessible to an observer confined to the system alone.
4. Conclusion
Decoherence as coherence decay is a cornerstone of modern quantum mechanics, providing a natural explanation for the quantum-to-classical transition. The process occurs due to the interaction of a quantum system with its environment, leading to the decay of off-diagonal elements in the density matrix. By erasing quantum phase relationships, decoherence suppresses interference effects and yields behaviour that aligns with classical physics.
Understanding the dynamics of coherence decay is not only essential for foundational physics but also critical for advancing quantum technologies. Future research should aim to control and mitigate decoherence, enabling the realization of robust quantum systems for computation, communication, and sensing.
References
1. Zurek, W. H. (2003). Decoherence and the transition from quantum to classical. Physics Today, 44(10), 36–44.
2. Joos, E., & Zeh, H. D. (1985). The emergence of classical properties through interaction with the environment. Zeitschrift für Physik B Condensed Matter, 59(2), 223–243.
3. Breuer, H. P., & Petruccione, F. (2007). The Theory of Open Quantum Systems. Oxford University Press.
4. Schlosshauer, M. (2007). Decoherence and the Quantum-to-Classical Transition. Springer.
5. Riedel, C. J., Zurek, W. H., & Zwolak, M. (2012). The rise and fall of quantum and classical correlations in quantum Darwinism. Nature Physics, 8(6), 393–397.
6. Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.
7. Giulini, D., Kiefer, C., & Zeh, H. D. (1996). Decoherence, irreversibility, and the emergence of classical properties. Physics Letters A, 222(3), 171–176.
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