A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Simulability of observables in general probabilistic theories
Tekijät: Filippov SN, Heinosaari T, Leppajarvi L
Kustantaja: AMER PHYSICAL SOC
Julkaisuvuosi: 2018
Journal: Physical Review A
Tietokannassa oleva lehden nimi: PHYSICAL REVIEW A
Lehden akronyymi: PHYS REV A
Artikkelin numero: ARTN 062102
Vuosikerta: 97
Numero: 6
Sivujen määrä: 19
ISSN: 2469-9926
eISSN: 2469-9934
DOI: https://doi.org/10.1103/PhysRevA.97.062102
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/32121877
Tiivistelmä
The existence of incompatibility is one of the most fundamental features of quantum theory and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A scheme for obtaining new observables from existing ones via classical operations, the so-called simulation of observables, has led to an extension of the notion of compatibility for measurements. We consider the simulation of observables within the operational framework of general probabilistic theories and introduce the concept of simulation irreducibility. While a simulation irreducible observable can only be simulated by itself, we show that any observable can be simulated by simulation irreducible observables, which in the quantum case correspond to extreme rank-1 positive-operator-valued measures. We also consider cases where the set of simulators is restricted in one of two ways: in terms of either the number of simulating observables or their number of outcomes. The former is seen to be closely connected to compatibility and k compatibility, whereas the latter leads to a partial characterization for dichotomic observables. In addition to the quantum case, we further demonstrate these concepts in state spaces described by regular polygons.
The existence of incompatibility is one of the most fundamental features of quantum theory and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A scheme for obtaining new observables from existing ones via classical operations, the so-called simulation of observables, has led to an extension of the notion of compatibility for measurements. We consider the simulation of observables within the operational framework of general probabilistic theories and introduce the concept of simulation irreducibility. While a simulation irreducible observable can only be simulated by itself, we show that any observable can be simulated by simulation irreducible observables, which in the quantum case correspond to extreme rank-1 positive-operator-valued measures. We also consider cases where the set of simulators is restricted in one of two ways: in terms of either the number of simulating observables or their number of outcomes. The former is seen to be closely connected to compatibility and k compatibility, whereas the latter leads to a partial characterization for dichotomic observables. In addition to the quantum case, we further demonstrate these concepts in state spaces described by regular polygons.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
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