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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 ...
Since the trace is only over a subspace, it is technically called a partial trace. Key to this step is that the (partial) trace adequately summarizes the system from Bob's point of view. That is, everything that Bob has access to, or could ever have access to, measure, or detect, is completely described by a partial trace over H A of the system ...
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 .
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
Moreover, a mixed quantum state on a given quantum system described by a Hilbert space can be always represented as the partial trace of a pure quantum state (called a purification) on a larger bipartite system for a sufficiently large Hilbert space .
In classical scattering of a target body by environmental photons, the motion of the target body will not be changed by the scattered photons on the average. In quantum scattering, the interaction between the scattered photons and the superposed target body will cause them to be entangled, thereby delocalizing the phase coherence from the target body to the whole system, rendering the ...
In quantum mechanics, and especially quantum information theory, the purity of a normalized quantum state is a scalar defined as ... (see partial trace).
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 ...