The apparent contradiction between the preservation of information in quantum theory and the loss of information during measurement is known as the measurement problem or the measurement paradox. Resolving this paradox has been a subject of intense debate and investigation in the field of quantum foundations.
In standard quantum mechanics, the time evolution of a quantum system is described by a unitary operator, which is reversible and preserves information. This principle is often referred to as the unitarity of quantum evolution. It implies that the evolution of a closed quantum system, where no measurement or interaction with the external world occurs, is deterministic and preserves all information about the system.
However, when a measurement is made on a quantum system, the measured value appears to be selected randomly according to the probabilities given by the wave function. This process, known as wave function collapse or projection postulate, appears to involve a loss of information about the superposition of possible measurement outcomes prior to the measurement.
Several interpretations and approaches have been proposed to reconcile these seemingly contradictory aspects of quantum theory. Here are a few prominent perspectives:
Many-Worlds Interpretation: According to the Many-Worlds Interpretation, proposed by Hugh Everett III, the wave function collapse does not actually occur. Instead, when a measurement is made, the universe branches into multiple copies, each corresponding to a different measurement outcome. In this view, all possible measurement outcomes are realized in different branches, preserving the unitary evolution and the information of the entire system.
Decoherence: Decoherence is a process in which a quantum system interacts with its environment, causing the superposition of states to rapidly lose coherence. While the system-environment interaction is deterministic and preserves information, the loss of coherence makes the different states effectively unobservable. Decoherence provides an explanation for the apparent collapse and the classical appearance of measurement outcomes, without actual loss of information.
Quantum Bayesianism (QBism): QBism takes a subjective Bayesian view of quantum mechanics, emphasizing the role of the observer's beliefs and probabilities. In this perspective, the measurement outcome is seen as an update to the observer's knowledge or belief, rather than a fundamental collapse of the wave function. Information loss occurs in the sense that the observer's belief about the system is updated to a specific outcome.
Consistent Histories: Consistent Histories is an approach that aims to provide a complete description of quantum systems by defining consistent sets of histories that obey specific consistency conditions. In this framework, measurements are treated as interactions between the system and the measuring apparatus, and the evolution is described consistently without invoking wave function collapse.
It's important to note that these interpretations and approaches are still the subject of active research and debate, and there is no widely accepted resolution to the measurement problem at present. The reconciliation between the preservation of information in quantum theory and the apparent loss of information in measurements remains an area of ongoing investigation in the field of quantum foundations.