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The partial trace can be viewed as a quantum operation. Consider a quantum mechanical system whose state space is the tensor product H A ⊗ H B {\displaystyle H_{A}\otimes H_{B}} of Hilbert spaces. A mixed state is described by a density matrix ρ , that is a non-negative trace-class operator of trace 1 on the tensor product H A ⊗ H B ...
Then the partial trace of , with respect to either system A or B, is a diagonal matrix whose non-zero diagonal elements are | |. In other words, the Schmidt decomposition shows that the reduced states of ρ {\displaystyle \rho } on either subsystem have the same spectrum.
Quantum tomography is a process by which, given a set of data representing the results of quantum measurements, a density matrix consistent with those measurement results is computed. [ 25 ] [ 26 ] When analyzing a system with many electrons, such as an atom or molecule , an imperfect but useful first approximation is to treat the electrons as ...
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
QuTiP, short for the Quantum Toolbox in Python, is an open-source computational physics software library for simulating quantum systems, particularly open quantum systems. [1] [2] QuTiP allows simulation of Hamiltonians with arbitrary time-dependence, allowing simulation of situations of interest in quantum optics, ion trapping, superconducting circuits and quantum nanomechanical resonators.
In quantum mechanics, quantum states are described by density matrices, which are certain trace class operators. [ 1 ] Trace-class operators are essentially the same as nuclear operators , though many authors reserve the term "trace-class operator" for the special case of nuclear operators on Hilbert spaces and use the term "nuclear operator ...
In quantum mechanics, negativity is a measure of quantum entanglement which is easy to compute. It is a measure deriving from the PPT criterion for separability. [1] It has been shown to be an entanglement monotone [2] [3] and hence a proper measure of entanglement.
Quantum state tomography is a process by which, given a set of data representing the results of quantum measurements, a quantum state consistent with those measurement results is computed. [50] It is named by analogy with tomography , the reconstruction of three-dimensional images from slices taken through them, as in a CT scan .