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Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics , including consistent histories and ...
In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has numerous applications in quantum information theory , for example in entanglement characterization and in state purification , and plasticity .
the reduced state of ρ on system A, ρ A, is obtained by taking the partial trace of ρ with respect to the B system: =. The partial trace operation is a CPTP map, therefore a quantum channel in the Schrödinger picture. [5] In the Heisenberg picture, the dual map of this channel is
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In this case, even entangled states can be written as a mixture of tensor products of single-party aphysical states, very similar to the form of separable states. In the qubit case, M k {\displaystyle M_{k}} are physical density matrices, which is consistent with the fact that for two qubits all PPT states are separable.
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Consider a quantum system that can be divided into two parts, A and B, such that independent measurements can be made on either part. The state space of the entire quantum system is then the tensor product of the spaces for the two parts. :=. Let ρ AB be a density matrix acting on states in H AB.
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