抽象Hilbert空间中层析的意义与解释
On the meaning and interpretation of Tomography in abstract Hilbert spaces
摘要：
阐明了用标准概率（层析概率）代替波函数或密度矩阵描述量子态的机理。量子层析成像是在一个抽象的希尔伯特空间框架下，通过厄米特线性算子在希尔伯特空间的单位分解，以迹公式表示算子的标积.分解的身份被认为是相对于过完整的家庭的投影机标记的额外的参数和包含的措施，取决于这些参数。它扮演Gram-Schmidt正交归一化核的角色。当测度等于1时，恒等式的分解与正算子值测度（POVM）分解一致。自旋层析成像，光子数层析成像和辛层析成像的例子被重新考虑在这个新的框架。
英文摘要：
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity decompositions in the Hilbert space of hermitian linear operators, with trace formula as scalar product of operators. Decompositions of identity are considered with respect to over-complete families of projectors labeled by extra parameters and containing a measure, depending on these parameters. It plays the role of a Gram-Schmidt orthonormalization kernel. When the measure is equal to one, the decomposition of identity coincides with a positive operator valued measure (POVM) decomposition. Examples of spin tomography, photon number tomography and symplectic tomography are reconsidered in this new framework.
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