27 research outputs found
Selective and efficient quantum process tomography in arbitrary finite dimension
The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows one to acknowledge errors in the implementations of quantum algorithms; on the other, it allows one to characterize unknown processes occurring in nature. Bendersky, Pastawski, and Paz [A. Bendersky, F. Pastawski, and J. P. Paz, Phys. Rev. Lett. 100, 190403 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.190403; Phys. Rev. A 80, 032116 (2009)PLRAAN1050-294710.1103/PhysRevA.80.032116] introduced a method to selectively and efficiently measure any given coefficient from the matrix description of a quantum channel. However, this method heavily relies on the construction of maximal sets of mutually unbiased bases (MUBs), which are known to exist only when the dimension of the Hilbert space is the power of a prime number. In this article, we lift the requirement on the dimension by presenting two variations of the method that work on arbitrary finite dimensions: one uses tensor products of maximal sets of MUBs, and the other uses a dimensional cutoff of a higher prime power dimension.Fil: Perito, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Roncaglia, Augusto Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Bendersky, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentin
General theory of measurement with two copies of a quantum state
We analyze the possible results of the most general measurement on two copies
of a quantum state. We show that can label a set of outcomes of such
measurement if and only if there is a family of completely co--positive (ccP)
maps such that the probability of occurrence is the
fidelity of the map , i.e. which must
add up to the fully depolarizing map. This implies that a POVM on two copies
induces a measure on the set of ccP maps (i.e., a ccPMVM). We present examples
of ccPMVM's and discuss their tomographic applications showing that two copies
of a state provide an exponential improvement in the efficiency of quantum
state tomography. This enables the existence of an efficient universal
detector.Comment: 4 pages, 1 figur
Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies
We present in a unified manner the existing methods for scalable partial
quantum process tomography. We focus on two main approaches: the one presented
in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones
described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and
L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined
together. The methods share an essential feature: They are based on the idea
that the tomography of a quantum map can be efficiently performed by studying
certain properties of a twirling of such a map. From this perspective, in this
paper we present extensions, improvements and comparative analyses of the
scalable methods for partial quantum process tomography. We also clarify the
significance of the extracted information, and we introduce interesting and
useful properties of the -matrix representation of quantum maps that can
be used to establish a clearer path toward achieving full tomography of quantum
processes in a scalable way.Comment: Replaced with published version (only minor changes respect to the
first version
Towards exact algorithmic proofs of maximal mutually unbiased bases sets in arbitrary integer dimension
In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in
discrete quantum systems. It is known that for dimensions that are powers
of prime numbers, there exists a set of up to bases that form an MUB set.
However, the maximum number of MUBs in dimensions that are not powers of prime
numbers is not known.
To address this issue, we introduce three algorithms based on First-Order
Logic that can determine the maximum number of bases in an MUB set without
numerical approximation. Our algorithms can prove this result in finite time,
although the required time is impractical. Additionally, we present a heuristic
approach to solve the semi-decision problem of determining if there are
MUBs in a given dimension .
As a byproduct of our research, we demonstrate that the maximum number of
MUBs in any dimension can be achieved with definable complex parameters,
computable complex parameters, and other similar fields.Comment: 11 pages, 0 figure