Quantum Measurement

Full Title

Quantum Measurement is the process of obtaining information about a quantum system, such as its position or momentum. This process involves interacting with the system and causing it to collapse from a superposition of states to a single definite state.

Context

• Eigenstates and Eigenvalues: When a measurement is performed, the system collapses to one of the eigenstates of the observable, and the measurement result is the corresponding eigenvalue.
• Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
• State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wavefunction.

Issues

First kind of quantum measurement

The first kind of quantum measurement, also known as the projective measurement, is a measurement that completely collapses the quantum system into one of its possible states. This type of measurement is irreversible and provides a definite outcome.

Second kind of quantum measurement

Non-demolition measurement is a type of quantum measurement that does not entirely collapse the system, but instead provides information about the system while still preserving its superposition of states. This type of measurement is used in quantum systems that require continuous monitoring without disturbing the system. What is the difference between the first kind and non-demolition measurement? The main difference between the first kind and non-demolition measurement is the effect they have on the quantum system. First kind measurements completely collapse the system, while non-demolition measurements only provide partial information while preserving the superposition of states. Non-demolition measurements are also reversible, while first kind measurements are irreversible.