Mixed State QM: Unpacking the Non-Diagonal Density Matrix

Thread starter daneshvar
Start date Apr 17, 2010
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Density Density matrix Matrix Mixed Mixed state Qm State

In summary, a mixed state in quantum mechanics is a non-diagonal density matrix that represents a combination of multiple pure states. This is different from a pure state, which is described by a diagonal density matrix. The non-diagonal elements of a mixed state's density matrix represent the phenomenon of superposition and determine the measurement outcomes. Unlike in a pure state, the measurement outcomes in a mixed state are probabilistic. It is possible to convert a mixed state into a pure state through the process of quantum purification, but this is not always feasible.

Apr 17, 2010

daneshvar

what do the non-diagonal components of a density matrix tell us about the mixed state we are in?

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Apr 17, 2010

Andy Resnick

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The non-diagonal components correspond to the transition probabilities, IIRC.

1. What is a mixed state in quantum mechanics?

A mixed state in quantum mechanics is a state of a quantum system that is described by a non-diagonal density matrix, meaning that it is a combination of multiple pure states. This is in contrast to a pure state, which is described by a diagonal density matrix.

2. How is a mixed state represented mathematically?

In quantum mechanics, a mixed state is represented by a density matrix, which is a matrix that contains the probabilities of finding the system in each of its possible pure states. The off-diagonal elements of the matrix represent the correlations between different pure states.

3. What is the significance of the non-diagonal elements in a mixed state's density matrix?

The non-diagonal elements of a mixed state's density matrix represent the quantum mechanical phenomenon of superposition, where the system exists in multiple states simultaneously. These elements also determine the measurement outcomes of the system, as they affect the probabilities of finding the system in each pure state.

4. How does a mixed state differ from a pure state in terms of measurement outcomes?

In a pure state, the measurement outcomes are deterministic and can be predicted with certainty. However, in a mixed state, the measurement outcomes are probabilistic, as the system is in a superposition of multiple pure states. This means that the outcome of a measurement cannot be predicted with certainty, but only with a certain probability.

5. Can a mixed state be converted into a pure state?

Yes, a mixed state can be converted into a pure state through a process called "quantum purification". This involves entangling the system with an external system, such as a measurement apparatus, to create a pure state. However, this process is not always possible and depends on the initial state of the system and the external system.