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ber70
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Is entangle enough to find that given states have Schmidt decomposition?
ber70 said:Why didn't anyone reply me?
Schmidt decomposition is a mathematical technique used in quantum mechanics to express a composite quantum state as a linear combination of product states. It allows us to understand the entanglement between different subsystems in a quantum system.
Schmidt decomposition involves finding the eigenvalues and eigenvectors of the reduced density matrix for a given quantum state. The eigenvectors represent the product states that make up the composite state, and the corresponding eigenvalues give the coefficients for each product state in the linear combination.
Schmidt decomposition is important because it allows us to analyze the entanglement between different subsystems in a quantum system. This is crucial for understanding and predicting the behavior of quantum systems, as entanglement plays a key role in many quantum phenomena.
No, Schmidt decomposition is not always enough to fully describe a quantum state. It is only applicable to pure states, which are idealized representations of quantum systems. In reality, many quantum systems are mixed states, which cannot be fully described by Schmidt decomposition alone.
There are some limitations to Schmidt decomposition. As mentioned earlier, it is only applicable to pure states and cannot fully describe mixed states. Additionally, it can be computationally expensive for large quantum systems, making it difficult to apply in certain situations.