In functional analysis and quantum information science, a positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalization of projection-valued measures (PVM) and, correspondingly, quantum measurements described by POVMs are a generalization of quantum measurement described by PVMs (called projective measurements).
In rough analogy, a POVM is to a PVM what a mixed state is to a pure state. Mixed states are needed to specify the state of a subsystem of a larger system (see purification of quantum state); analogously, POVMs are necessary to describe the effect on a subsystem of a projective measurement performed on a larger system.
POVMs are the most general kind of measurement in quantum mechanics, and can also be used in quantum field theory.[1] They are extensively used in the field of quantum information.
^Peres, Asher; Terno, Daniel R. (2004). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. S2CID 7481797.
positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalization of projection-valued...
positive-operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalisation of projection-valued...
positive-operator-valued measures (POVM). A POVM is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalization of...
, the most general possible measurement they can make on the state is a POVM, which is described by a set of Hermitian positive semidefinite operators...
performed over all POVMs Π ≡ { Π i } i {\displaystyle \Pi \equiv \{\Pi _{i}\}_{i}} . To conclude that the inequality is saturated by some POVM, we need only...
JSTOR 27854250. Bengtsson, Ingemar (2017). "The Number Behind the Simplest SIC-POVM". Foundations of Physics. 47 (8): 1031–41. arXiv:1611.09087. Bibcode:2017FoPh...
{E}}_{i}} , but the above definition of the POVM elements M i {\displaystyle M_{i}} is the same for any choice. The POVM can be thought of as the measurement...
positive operator-valued measures (POVM), which is the most general kind of measurement in quantum mechanics. A POVM can be understood as the effect on...
is a minimal, informationally complete positive operator-valued measure (POVM), this is especially clear: A quantum state is mathematically equivalent...
i F i = I {\textstyle \sum _{i}F_{i}=I} . (Such a collection is called a POVM.) In the Heisenberg picture, the corresponding observable map Ψ {\displaystyle...
probability of the POVM ( E i ) i {\displaystyle (E_{i})_{i}} correctly guessing which state was received. Since the probability of the POVM returning the...
{\displaystyle R} , then V {\displaystyle V} is smooth. Zauner's conjecture: do SIC-POVMs exist in all dimensions? Zilber–Pink conjecture that if X {\displaystyle...
positive operator-valued measures (POVMs) describe the effect on a subsystem of a measurement performed on a larger system. POVMs are extensively used in quantum...
Teleportation Fidelity of quantum teleportation through noisy channels by TelePOVM – A generalized quantum teleportation scheme Entanglement Teleportation via...
313–354. ISBN 978-1-107-02625-4. OCLC 967938939. Zhu, Huangjun (2010). "SIC POVMs and Clifford groups in prime dimensions". Journal of Physics A: Mathematical...
several other branches of mathematics and quantum sciences, such as SIC-POVMs, finite projective/affine planes, complex Hadamard matrices and more [see...
results like Holevo's theorem, the concept of generalized measurements or POVMs, the proposal of quantum key distribution by Bennett and Brassard, and Shor's...
ρ {\displaystyle \rho } and σ {\displaystyle \sigma } . A strategy is a POVM with elements Q {\displaystyle Q} and I − Q {\displaystyle I-Q} . The probability...
combined system to recover the message. Let Bob's measurement be modelled by a POVM { F y } y {\displaystyle \{F_{y}\}_{y}} , with F y {\displaystyle F_{y}}...
\cdots ,X_{n}\}} , where the elements X i {\displaystyle X_{i}} make up a POVM and the set { a 1 , ⋯ , a n } {\displaystyle \{a_{1},\cdots ,a_{n}\}} are...
restriction on the dimension can be removed by assuming non-contextuality for POVMs as well, but this has been criticized as physically unmotivated. The von...
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