Ancilla-assisted discrimination of quantum gates

Chen, J; Ying, M

Ancilla-assisted discrimination of quantum gates

Chen, J Ying, M

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Publisher:: Rinton Press
Publication Type:: Journal Article
Citation:: Quantum Information and Computation, 2010, 10 (1), pp. 160 - 177
Issue Date:: 2010-01

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Field	Value	Language
dc.contributor.author	Chen, J	en_US
dc.contributor.author	Ying, M	en_US
dc.date.issued	2010-01	en_US
dc.identifier.citation	Quantum Information and Computation, 2010, 10 (1), pp. 160 - 177	en_US
dc.identifier.issn	1533-7146	en_US
dc.identifier.uri	http://hdl.handle.net/10453/13488
dc.description.abstract	The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding.	en_US
dc.publisher	Rinton Press	en_US
dc.relation.ispartof	Quantum Information and Computation	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Ancilla-assisted discrimination of quantum gates	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	10	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - Quantum Computation and Intelligent Systems
utslib.copyright.status	closed_access
pubs.consider-herdc	false	en_US
pubs.issue	1	en_US
pubs.volume	10	en_US

Abstract:

The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding.

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http://hdl.handle.net/10453/13488