Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (4)

Search Parameters:
Keywords = informationally-complete POVMs

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
11 pages, 1820 KiB  
Article
Estimating Molecular Thermal Averages with the Quantum Equation of Motion and Informationally Complete Measurements
by Daniele Morrone, N. Walter Talarico, Marco Cattaneo and Matteo A. C. Rossi
Entropy 2024, 26(9), 722; https://doi.org/10.3390/e26090722 - 23 Aug 2024
Cited by 4 | Viewed by 1041
Abstract
By leveraging the Variational Quantum Eigensolver (VQE), the “quantum equation of motion” (qEOM) method established itself as a promising tool for quantum chemistry on near-term quantum computers and has been used extensively to estimate molecular excited states. Here, we explore a novel application [...] Read more.
By leveraging the Variational Quantum Eigensolver (VQE), the “quantum equation of motion” (qEOM) method established itself as a promising tool for quantum chemistry on near-term quantum computers and has been used extensively to estimate molecular excited states. Here, we explore a novel application of this method, employing it to compute thermal averages of quantum systems, specifically molecules like ethylene and butadiene. A drawback of qEOM is that it requires measuring the expectation values of a large number of observables on the ground state of the system, and the number of necessary measurements can become a bottleneck of the method. In this work, we focus on measurements through informationally complete positive operator-valued measures (IC-POVMs) to achieve a reduction in the measurement overheads by estimating different observables of interest through the measurement of a single set of POVMs. We show with numerical simulations that the qEOM combined with IC-POVM measurements ensures satisfactory accuracy in the reconstruction of the thermal state with a reasonable number of shots. Full article
(This article belongs to the Special Issue Simulation of Open Quantum Systems)
►▼ Show Figures

Figure 1

9 pages, 286 KiB  
Communication
On Constructing Informationally Complete Covariant Positive Operator-Valued Measures
by Grigori Amosov
Entropy 2023, 25(5), 783; https://doi.org/10.3390/e25050783 - 11 May 2023
Cited by 2 | Viewed by 1446
Abstract
We study a projective unitary representation of the product G=G˜×G, where G is a locally compact Abelian group and G^ is its dual consisting of characters on G. It is proven that the representation is [...] Read more.
We study a projective unitary representation of the product G=G˜×G, where G is a locally compact Abelian group and G^ is its dual consisting of characters on G. It is proven that the representation is irreducible, which allows us to define a covariant positive operator-valued measure (covariant POVM) generated by orbits of projective unitary representations of G. The quantum tomography associated with the representation is discussed. It is shown that the integration over such a covariant POVM defines a family of contractions which are multiples of unitary operators from the representation. Using this fact, it is proven that the measure is informationally complete. The obtained results are illustrated by optical tomography on groups and by a measure with a density that has a value in the set of coherent states. Full article
(This article belongs to the Special Issue Quantum Information: From Fundamental Aspects to Practical Applications)
12 pages, 555 KiB  
Article
The Poincaré Half-Plane for Informationally-Complete POVMs
by Michel Planat
Entropy 2018, 20(1), 16; https://doi.org/10.3390/e20010016 - 31 Dec 2017
Cited by 9 | Viewed by 5338
Abstract
It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from [...] Read more.
It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincaré upper half-plane model H . To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
►▼ Show Figures

Figure 1

14 pages, 337 KiB  
Article
SIC-POVMs and Compatibility among Quantum States
by Blake C. Stacey
Mathematics 2016, 4(2), 36; https://doi.org/10.3390/math4020036 - 1 Jun 2016
Cited by 19 | Viewed by 6048
Abstract
An unexpected connection exists between compatibility criteria for quantum states and Symmetric Informationally Complete quantum measurements (SIC-POVMs). Beginning with Caves, Fuchs and Schack’s "Conditions for compatibility of quantum state assignments", I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting [...] Read more.
An unexpected connection exists between compatibility criteria for quantum states and Symmetric Informationally Complete quantum measurements (SIC-POVMs). Beginning with Caves, Fuchs and Schack’s "Conditions for compatibility of quantum state assignments", I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way to understand the relationship between SIC-POVMs and mutually unbiased bases, as calculations in the SIC representation of quantum states make clear. This, in turn, illuminates the resources necessary for magic-state quantum computation, and why hidden-variable models fail to capture the vitality of quantum mechanics. Full article
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop