Symmetric informationally complete measurements identify the irreducible difference between classical and quantum systems
نویسندگان
چکیده
منابع مشابه
Symmetric Informationally Complete Quantum Measurements
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d rank-one operators all of whose operator inner products are equal. Such a set is called a “symmetric, informationally complete” POVM (SIC-POVM) and is equivalent to a set of d equiangular lines in C . SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum me...
متن کاملTight informationally complete quantum measurements
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, “as close as possible” to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows “painless” quantum state tomography. Complete sets of mutually unbiased bases and symmetric i...
متن کاملSymmetric Informationally Complete Measurements of Arbitrary Rank
There has been much interest in so-called SIC-POVMs: rank 1 symmetric in-formationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM which is closely related to the discrete Wigner func...
متن کاملThe Lie algebraic significance of symmetric informationally complete measurements
Examples of symmetric informationally complete positive operator-valued measures (SIC-POVMs) have been constructed in every dimension ≤67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,...
متن کاملConstruction of all general symmetric informationally complete measurements
We construct the set of all general (i.e. not necessarily rank 1) symmetric informationally complete (SIC) positive operator valued measures (POVMs), and thereby show that SIC-POVMs that are not necessarily rank 1 exist in any finite dimension d. In particular, we show that any orthonormal basis of a real vector space of dimension d 2 − 1 corresponds to some general SIC POVM and vice versa. Our...
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ژورنال
عنوان ژورنال: Physical Review Research
سال: 2020
ISSN: 2643-1564
DOI: 10.1103/physrevresearch.2.013074