Araujo, Mateus, Guerin, Philippe Allard and Baumeler, Amin ORCID: 0000-0001-6760-0439 (2017). Quantum computation with indefinite causal structures. Phys. Rev. A, 96 (5). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9934

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Abstract

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and postselection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively. Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological. This problem is closely related to the nonlinearity of this models, which also allows, for example, cloning quantum states, in the case of D-CTCs, or distinguishing nonorthogonal quantum states, in the case of P-CTCs. In contrast, the process matrix formalism allows one to model indefinite causal structures in a linear way, getting rid of these effects and raising the possibility that its computational power is rather tame. In this paper, we show that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP. We show, furthermore, a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Araujo, MateusUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Guerin, Philippe AllardUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Baumeler, AminUNSPECIFIEDorcid.org/0000-0001-6760-0439UNSPECIFIED
URN: urn:nbn:de:hbz:38-211315
DOI: 10.1103/PhysRevA.96.052315
Journal or Publication Title: Phys. Rev. A
Volume: 96
Number: 5
Date: 2017
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2469-9934
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
TIME; MECHANICSMultiple languages
Optics; Physics, Atomic, Molecular & ChemicalMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/21131

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