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Negative quantum channels : an introduction to quantum maps that are not completely positive /
This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham, Switzerland :
Springer,
[2014]
|
| Colección: | Synthesis lectures on quantum computing ;
#7. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
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| 003 | OCoLC | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a McCracken, James M., |e author. | |
| 245 | 1 | 0 | |a Negative quantum channels : |b an introduction to quantum maps that are not completely positive / |c James M. McCracken. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xv, 171 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Synthesis lectures on quantum computing, |x 1945-9726 ; |v #7 | |
| 588 | 0 | |a Online resource; title from PDF title page (Morgan & Claypool, viewed on July 21, 2014). | |
| 504 | |a Includes bibliographical references (pages 161-169). | ||
| 505 | 0 | |6 880-01 |a Introduction and definition of terms -- Tomography -- Non-positive reduced dynamics -- Complete positivity -- Physical motivation of complete positivity -- Measures of complete positivity -- Negative channels -- Negative climates with diagonal composite dynamics -- Rabi channels -- Physical motivations for sharp operations -- Proposed experimental demonstration of negativity -- Implications of negative channels -- Uses for negative channels. | |
| 505 | 0 | |a 1. Introduction and definition of terms -- 1.1 Motivation -- 1.2 Open systems -- 1.3 Density matrix -- 1.4 Mathematical structure of open systems -- 1.4.1 System state spaces -- 1.4.2 Partial trace -- 1.4.3 Assignments of subsystem states -- 1.4.4 Reduced system dynamics -- 1.5 "Vector of states" notation. | |
| 505 | 8 | |a 2. Tomography. | |
| 505 | 8 | |a 3. Non-positive reduced dynamics -- 3.1 Two qubit SWAP example -- 3.2 Positivity domains interpretation. | |
| 505 | 8 | |a 4. Complete positivity -- 4.1 Complete positivity definition -- 4.2 Reduced system evolution as an operator sum. | |
| 505 | 8 | |a 5. Physical motivation of complete positivity -- 5.1 Total domain argument -- 5.2 Product state argument. | |
| 505 | 8 | |a 6. Measures of complete positivity -- 6.1 Local unitary composite evolution -- 6.2 Product composite states -- 6.3 Zero discord initial composite states -- 6.4 Completely positive reduced dynamics without a special form -- 6.5 Choi's matrix -- 6.6 Negativity. | |
| 505 | 8 | |a 7. Negative channels -- 7.1 Definitions -- 7.2 Sharp operations for negative channels. | |
| 505 | 8 | |a 8. Negative climates with diagonal composite dynamics -- 8.1 Specific negative channel example -- 8.2 Basis dependence. | |
| 505 | 8 | |a 9. Rabi channels -- 9.1 Rabi model -- 9.2 Rabi channels with no coupling -- 9.3 Rabi channels with coupling. | |
| 505 | 8 | |a 10. Physical motivations for sharp operations. | |
| 505 | 8 | |a 11. Negative qubit channel examples with multi-qubit baths. | |
| 505 | 8 | |a 12. Proposed experimental demonstration of negativity -- 12.1 Photonic root-swap operation -- 12.2 Photonic CZ operation. | |
| 505 | 8 | |a 13. Implications of negative channels -- 13.1 Existing experimental evidence of negative channels -- 13.2 Restrictions implied by complete positivity -- 13.3 Expanding the definition of "physically reasonable." | |
| 505 | 8 | |a 14. Uses for negative channels -- 14.1 Probing the bath -- 14.1.1 Coupling alone -- 14.1.2 Correlation alone -- 14.1.3 Coupling and correlation together -- 14.1.4 Determining the completely positive parameter space -- 14.2 Speculation on utilities. | |
| 505 | 8 | |a 15. Conclusions -- 15.1 Complete positivity in recent years -- 15.2 Closing remarks. | |
| 505 | 8 | |a A. Discussions -- Discussion of the reduced system definition -- General reduced system dynamics -- General form of initial reduced system state -- Completeness relation for SQO -- Rabi model derivation -- Bibliography -- Author's biography. | |
| 520 | 3 | |a This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that complete positivity is not a physical requirement of all quantum operations. Negativity, a measure of the lack of complete positivity, is proposed as a tool for empirically testing complete positivity assumptions. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Quantum maps. | |
| 650 | 0 | |a Quantum systems. | |
| 650 | 0 | |a Quantum computers. | |
| 650 | 6 | |a Applications quantiques. | |
| 650 | 6 | |a Systèmes quantiques. | |
| 650 | 6 | |a Ordinateurs quantiques. | |
| 650 | 7 | |a SCIENCE |x Energy. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Mechanics |x General. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Physics |x General. |2 bisacsh | |
| 650 | 7 | |a Quantum computers |2 fast | |
| 650 | 7 | |a Quantum maps |2 fast | |
| 650 | 7 | |a Quantum systems |2 fast | |
| 758 | |i has work: |a Negative quantum channels (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGTtmkdgcpdr9xVBTV6cWC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a McCracken, James M. |t Negative quantum channels. |d [San Rafael, California] : Morgan & Claypool Publishers, [2014] |z 9781627051842 |w (OCoLC)888559784 |
| 830 | 0 | |a Synthesis lectures on quantum computing ; |v #7. |x 1945-9734 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1743731 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Introduction and Definition of Terms -- |g 1.1. |t Motivation -- |g 1.2. |t Open Systems -- |g 1.3. |t Density Matrix -- |g 1.4. |t Mathematical Structure of Open Systems -- |g 1.4.1. |t System State Spaces -- |g 1.4.2. |t Partial Trace -- |g 1.4.3. |t Assignments of Subsystem States -- |g 1.4.4. |t Reduced System Dynamics -- |g 1.5. |t "Vector of States" Notation -- |g 2. |t Tomography -- |g 3. |t Non-Positive Reduced Dynamics -- |g 3.1. |t Two Qubit SWAP Example -- |g 3.2. |t Positivity Domains Interpretation -- |g 4. |t Complete Positivity -- |g 4.1. |t Complete Positivity Definition -- |g 4.2. |t Reduced System Evolution as an Operator Sum -- |g 5. |t Physical Motivation of Complete Positivity -- |g 5.1. |t Total Domain Argument -- |g 5.2. |t Product State Argument -- |g 6. |t Measures of Complete Positivity -- |g 6.1. |t Local Unitary Composite Evolution -- |g 6.2. |t Product Composite States -- |g 6.3. |t Zero Discord Initial Composite States -- |g 6.4. |t Completely Positive Reduced Dynamics without a Special Form -- |g 6.5. |t Choi's Matrix -- |g 6.6. |t Negativity -- |g 7. |t Negative Channels -- |g 7.1. |t Definitions -- |g 7.2. |t Sharp Operations for Negative Channels -- |g 8. |t Negative Climates with Diagonal Composite Dynamics -- |g 8.1. |t Specific Negative Channel Example: ([→]τ, [→]τ [⊗] (Hd : [→]τ : H[†]d), D) -- |g 8.2. |t ([→]τ, [→]τ [⊗] (Hd : [→]τ : H[†]d), D) Basis Dependence -- |g 9. |t Rabi Channels -- |g 9.1. |t Rabi Model -- |g 9.2. |t Rabi Channels with No Coupling -- |g 9.3. |t Rabi Channels with Coupling -- |g 10. |t Physical Motivations for Sharp Operations -- |g 11. |t Negative Qubit Channel Examples with Multi-Qubit Baths -- |g 12. |t Proposed Experimental Demonstration of Negativity -- |g 12.1. |t Photonic Root-Swap Operation -- |g 12.2. |t Photonic CZ Operation -- |g 13. |t Implications of Negative Channels -- |g 13.1. |t Existing Experimental Evidence of Negative Channels -- |g 13.2. |t Restrictions Implied by Complete Positivity -- |g 13.3. |t Expanding the Definition of "Physically Reasonable" -- |g 14. |t Uses for Negative Channels -- |g 14.1. |t Probing the Bath -- |g 14.1.1. |t Coupling Alone -- |g 14.1.2. |t Correlation Alone -- |g 14.1.3. |t Coupling and Correlation Together -- |g 14.1.4. |t Determining the Completely Positive Parameter Space -- |g 14.2. |t Speculation on Utilities -- |g 15. |t Conclusions -- |g 15.1. |t Complete Positivity in Recent Years -- |g 15.2. |t Closing Remarks -- |g A. |t Discussions -- |g A.1. |t Discussion of the Reduced System Definition -- |g A.2. |t General Reduced System Dynamics -- |g A.3. |t General Form of Initial Reduced System State -- |g A.4. |t Completeness Relation for Sqφ -- |g A.5. |t Rabi Model Derivation. |
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