Preface ........................................................ ix
Authors' addresses ............................................. xi
Many body effects and cluster state quantum computation in
strongly interacting systems of photons ......................... 1
Dimitris G. Angelakis, Sougato Bose, Alastair Kay
and Marcelo F. Santos
1. Introduction ................................................. 1
2. System Description ........................................... 2
2.1. Polaritonic Mott State .................................. 4
3. Simulating XY spin models .................................... 7
4. Cluster state quantum computation ............................ 8
4.1. Implementing algorithms ................................ 10
5. Experimental implementations ................................ 13
6. Conclusions ................................................. 14
References ..................................................... 14
A protocol for cooling and controlling composite systems by
local interactions ............................................. 17
Daniel Burgarth and Vittorio Giovannetti
1. Introduction ................................................ 17
2. The Protocol ................................................ 18
2.1. Downloading info from СС to M .......................... 18
2.2. Uploading info from M to СС ............................ 21
3. Coding transformation ....................................... 23
3.1. Fidelity of the downloading protocol ................... 25
3.2. Fidelity of the uploading protocol ..................... 26
4. Efficiency of Cooling ....................................... 27
5. Conclusion .................................................. 30
A. Evolution of С .............................................. 30
В. Decomposition equations ..................................... 31
References ..................................................... 32
Area laws and entanglement distillability of thermal states .... 35
Daniel Cavalcanti, Alessandro Ferraro, Artur Garcfa-Saez
and Antonio Acin
1. Introduction ................................................ 35
2. Bound entanglement and area laws ............................ 38
3. Harmonic Oscillators ........................................ 40
4. Spin systems ................................................ 44
5. Conclusions ................................................. 48
References ..................................................... 48
Locality of dynamics in general harmonic quantum systems ....... 51
Marcus Cramer, Alessio Serafini and Jens Eisert
1. Introduction ................................................ 51
2. Considered models and main results .......................... 54
2.1. Local couplings ........................................ 55
2.2. Application: Non-relativistic quantum mechanics
yields causality in the field limit .................... 58
2.3. Non-local couplings .................................... 60
2.4. Weyl operators ......................................... 62
2.5. More general operators ................................. 64
3. Proofs ...................................................... 65
3.1. Preliminaries .......................................... 65
3.2. Local couplings ........................................ 66
3.3. Non-local couplings .................................... 68
3.4. Weyl operators ......................................... 69
4. Summary ..................................................... 71
References ..................................................... 72
Giampaolo and Fabrizio llluminati Ground-state
factorization in spin-1/2 systems by single qubit
unitary operations and entanglement excitation energies ........ 75
1. Introduction ................................................ 75
2. SQUOs, separability, and entanglement ....................... 79
3. Excitation energies associated to generic SQUOs ............. 80
4. Entanglement excitation energies associated
to extremal SQUOs ........................................... 86
5. Conclusion .................................................. 90
References ..................................................... 92
Spin chains, operator algebras and entanglement.
A beginners introduction ....................................... 95
Michael Keyl
1. Introduction ................................................ 95
2. Algebras .................................................... 97
3. Representations ............................................. 99
4. States ..................................................... 101
5. Distillation of entanglement ............................... 105
6. Split property and infinite entanglement ................... 108
7. Localization properties .................................... 110
8. Example: The critical XY model ............................. 111
References .................................................... 114
Entanglement entropy and the simulation of Quantum
Mechanics ..................................................... 117
Jose I.Latorre
1. Entanglement entropy as a measure of quantum
correlations ............................................... 117
2. Refutation of the need for exponential resources ........... 119
3. Matrix product sates ....................................... 119
4. Entropy and matrix product states for spin chains .......... 122
5. New applications on matrix product sates:
continuous variables, Laughlin state, quantum
computation ................................................ 123
6. Spin-off: image compression, differential equations ........ 125
7. Beyond MPS: MERA and PEPs .................................. 125
References .................................................... 126
Gaussian matrix product states ................................ 129
Norbert Schuch, Michael M.Wolf and J.Ignacio Cirac
1. Introduction ............................................... 129
2. Gaussian states ............................................ 130
3. Gaussian Matrix Product States ............................. 132
4. Completeness of Gaussian MPS ............................... 134
5. GMPS with finitely entangled bonds ......................... 135
6. Correlation functions of Gaussian MPS ...................... 137
7. States with rational trigonometric functions
as Fourier transforms ...................................... 139
8. Correlation length ......................................... 140
9. Gaussian MPS as ground states of local Hamiltonians ........ 141
References ................................................. 141
Extended quantum annealing and quantum algorithms
for optimization and thermodynamics of classical systems ...... 143
Rolando D.Somma, Cristian D.Batista and Gerardo Ortiz
1. Introduction ............................................... 143
2. Classical-to-quantum mapping ............................... 146
3. Unifying framework for different optimization
strategies: Rates of convergence and the adiabatic
theorem of Quantum Mechanics ............................... 148
4. Quantum algorithms for numerical integration
with no importance-sampling ................................ 153
5. Conclusions ................................................ 155
References .................................................... 156
The fidelity approach to quantum phase transitions ............ 159
Paolo Zanardi
1. Introduction ............................................... 159
2. The metric approach ........................................ 160
3. Quasi-free fermionic systems ............................... 163
4. Correlation function representation and scaling
relations .................................................. 165
5. Finite temperature phase transitions ....................... 166
6. Classical phase transitions ................................ 168
7. Outlook .................................................... 169
References .................................................... 170
|
