Computing stabilized norms for quantum operations

2009 ◽  
Vol 9 (1&2) ◽  
pp. 16-36
Author(s):  
N. Johnston ◽  
D.W. Kribs ◽  
V.I. Paulsen
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Distance Measures ◽  
Quantum Information Science ◽  
Linear Map ◽  
Quantum Operations ◽  
Linear Maps

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. We give a brief introduction to the theory of completely bounded maps. Based on this theory, we formulate an algorithm to compute the norm of an arbitrary linear map. We present an implementation of the algorithm via MATLAB, discuss its efficiency, and consider the case of differences of unitary maps.

LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES

2014 ◽  
Vol 98 (3) ◽  
pp. 407-428 ◽  
Author(s):  
JINLI XU ◽  
BAODONG ZHENG ◽  
AJDA FOŠNER
Keyword(s):  
Quantum Information ◽  
Positive Integer ◽  
Information Science ◽  
Tensor Products ◽  
Hermitian Matrices ◽  
Quantum Information Science ◽  
Linear Maps ◽  
Rank One ◽  
Image Position ◽  
Positive Integers

For a positive integer $n\geq 2$, let $M_{n}$ be the set of $n\times n$ complex matrices and $H_{n}$ the set of Hermitian matrices in $M_{n}$. We characterize injective linear maps ${\it\phi}:H_{m_{1}\cdots m_{l}}\rightarrow H_{n}$ satisfying $$\begin{eqnarray}\text{rank}(A_{1}\otimes \cdots \otimes A_{l})=1\Longrightarrow \text{rank}({\it\phi}(A_{1}\otimes \cdots \otimes A_{l}))=1\end{eqnarray}$$ for all $A_{k}\in H_{m_{k}}$, $k=1,\dots ,l$, where $l,m_{1},\dots ,m_{l}\geq 2$ are positive integers. The necessity of the injectivity assumption is shown. Moreover, the connection of the problem to quantum information science is mentioned.

Quantum Information Science

2012 ◽  
Author(s):  
Paul M. Alsing ◽  
Michael L. Fanto
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science

Colloidal Quantum Dots as Platforms for Quantum Information Science

2020 ◽  
Author(s):  
Cherie R. Kagan ◽  
Lee C. Bassett ◽  
Christopher B. Murray ◽  
Sarah M. Thompson
Keyword(s):  
Quantum Dots ◽  
Quantum Information ◽  
Information Science ◽  
Colloidal Quantum Dots ◽  
Quantum Information Science

B800–B850 coherence correlates with energy transfer rates in the LH2 complex of photosynthetic purple bacteria

2015 ◽  
Vol 17 (46) ◽  
pp. 30805-30816 ◽  
Author(s):  
Cathal Smyth ◽  
Daniel G. Oblinsky ◽  
Gregory D. Scholes
Keyword(s):  
Energy Transfer ◽  
Quantum Information ◽  
Information Science ◽  
Light Harvesting ◽  
Purple Bacteria ◽  
Quantum Information Science ◽  
Light Harvesting Complex ◽  
Transfer Rates ◽  
Photosynthetic Purple Bacteria

Delocalization of a model light-harvesting complex is investigated using multipartite measures inspired by quantum information science.

Quantum Information Science, Introduction to

2012 ◽  
pp. 2534-2535
Author(s):  
Joseph F. Traub
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science

Half-cycle in quantum information science

2004 ◽  
Author(s):  
S. Pisharody ◽  
J. Murray ◽  
H. Wen ◽  
P. Bucksbaum
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Half Cycle ◽  
Quantum Information Science

scholarly journals Physical Implementability of Linear Maps and Its Application in Error Mitigation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 600
Author(s):  
Jiaqing Jiang ◽  
Kun Wang ◽  
Xin Wang
Keyword(s):  
General Linear ◽  
Local Error ◽  
Decomposition Technique ◽  
Completely Positive ◽  
Linear Map ◽  
Quantum Operations ◽  
Error Mitigation ◽  
Linear Maps ◽  
Analytic Expressions ◽  
Sampling Cost

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. This raises the question of how well one can simulate or approximate the action of a general linear map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition technique. We decompose a target linear map into a linear combination of physically implementable operations and introduce the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which directly quantifies the cost of simulating a given map using physically implementable quantum operations. We show this measure is efficiently computable by semidefinite programs and prove several properties of this measure, such as faithfulness, additivity, and unitary invariance. We derive lower and upper bounds in terms of the Choi operator's trace norm and obtain analytic expressions for several linear maps of practical interests. Furthermore, we endow this measure with an operational meaning within the quantum error mitigation scenario: it establishes the lower bound of the sampling cost achievable via the quasiprobability decomposition technique. In particular, for parallel quantum noises, we show that global error mitigation has no advantage over local error mitigation.

On the efficacy of classical deep learning methods on quantum information science

2021 ◽  
Author(s):  
Sanjaya Lohani ◽  
Brian T. Kirby ◽  
Ryan T. Glasser ◽  
Thomas A. Searles
Keyword(s):  
Deep Learning ◽  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science ◽  
Learning Methods

Invitation to Quantum Information Science

2014 ◽  
pp. 1-12
Author(s):  
Masahito Hayashi ◽  
Satoshi Ishizaka ◽  
Akinori Kawachi ◽  
Gen Kimura ◽  
Tomohiro Ogawa
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science
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