Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement.

Scientific Reports
Zhou ZhangChengjie Zhang

Abstract

Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. On the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-qubit states, single-qutrit states, and a special kind of d-dimensional mixed states. Moreover, we also obtain an analytical solution of geometric measure of coherence for a special kind of mixed states. On the other hand, another algorithm is proposed to calculate the geometric measure of entanglement for arbitrary two-qubit and qubit-qutrit states, and some special kinds of higher dimensional mixed states. For other states, the algorithm can get a lower bound of the geometric measure of entanglement. Randomly generated two-qubit states, the isotropic states and the Werner states are tested. Furthermore, we compare our numerical results with some analytical results, which coincide with each other.

References

Oct 15, 1989·Physical Review A: General Physics·R F Werner
Aug 19, 1996·Physical Review Letters·A Peres
May 15, 2002·Physical Review Letters·A C DohertyFederico M Spedalieri
Jan 7, 2003·Physical Review Letters·Th Richter, W Vogel
May 21, 2005·Physical Review Letters·János K AsbóthHelmut Ritsch
Jun 15, 2011·Physical Review Letters·Bastian JungnitschOtfried Gühne
Oct 18, 2014·Physical Review Letters·T BaumgratzM B Plenio
Nov 8, 2014·Physical Review Letters·Davide Girolami
May 9, 2015·Physical Review Letters·Géza TóthOtfried Gühne
Jun 13, 2015·Physical Review Letters·Thomas R BromleyGerardo Adesso
Jul 26, 2015·Physical Review Letters·Alexander StreltsovGerardo Adesso
Apr 9, 2016·Physical Review Letters·Andreas Winter, Dong Yang
Apr 30, 2016·Physical Review Letters·Carmine NapoliGerardo Adesso
Jan 28, 2017·Physical Review Letters·Yi-Tao WangGuang-Can Guo
Aug 18, 2018·Physical Review Letters·Kang-Da WuMile Gu
Apr 24, 2019·Physical Review Letters·Roope UolaOtfried Gühne
Nov 26, 2019·Physical Review Letters·Chao ZhangGerardo Adesso

❮ Previous
Next ❯

Software Mentioned

SDPT3
MATLAB
Matlab parser
YALMIP
SEDUMI

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.