- #1
Dragonfall
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What is the difference between a mixed state and a superposition?
comote said:[tex]\psi=\lambda_1\psi_1+\lambda_2\psi_2[/tex] is a superposition of two vectors but is generally still regarded as a pure state. Technically the density operator
[tex]|\psi\rangle\langle\psi|[/tex] is a pure state.
Where as the density operator
[tex]\lambda_1|\psi_1\rangle\langle\psi_1|+\lambda_2|\psi_2\rangle\langle\psi_2|[/tex]
is a mixed state.
Dragonfall said:How do you express a mixed state using vectors?
A mixed state refers to a quantum system that is described by a probabilistic combination of multiple pure states. In contrast, superposition refers to a quantum system that exists in a combination of two or more pure states simultaneously.
2)No, a system can only be in either a mixed state or superposition at a given time. The two concepts are mutually exclusive and describe different types of quantum systems.
3)A classical probability distribution describes the uncertainty of a classical system, while a mixed state describes the uncertainty of a quantum system. In a classical probability distribution, the uncertainty arises from a lack of knowledge about the system, while in a mixed state, the uncertainty is inherent in the quantum nature of the system.
4)Measurement plays a crucial role in determining the state of a system in superposition. When a measurement is made, the superposition collapses into one of the possible pure states, and the outcome of the measurement is one of the possible values associated with that state.
5)While superposition is a fundamental concept in quantum mechanics, its effects are usually only observed at the microscopic level. Macroscopic objects are typically described by classical mechanics and do not exhibit the same quantum behaviors as subatomic particles.