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note
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The usual Kronecker matrix representation uses the following lexicographic ordering for the basis of the tensor-product Hilbert space: the basis element |i>⊗|j> precedes |k>⊗|l> if and only if either i
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19
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0347959201
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note
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Notice that the isomorphism R≡L of the two ancillary Hilbert spaces does not mean that the two ancillas are physically equivalent, but only that there exist unitary realizations with the same physical ancilla. In fact, the ancillary spaces can be embedded in different ways in the overall tensor product, different embeddings can be included in the operator of the unitary interaction with the system. These kinds of ambiguity are due to the implicit identification between physical quantum system and its Hilbert space of states within a multipartite (i.e., tensor product) composite system. The misidentification is resolved by more properly identifying the quantum system with its algebra of observables.
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26
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85088493466
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note
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n/∼.
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