ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

Contents xiii
10.1.1. The “allotment” box for engineering arbitrary three-mode pure
states 175
10.1.2. Tripartite state engineering handbook and simplified schemes 179
10.1.2.1. CV GHZ/W states 179
10.1.2.2. Noisy GHZ/W states 180
10.1.2.3. T states 181
10.1.2.4. Basset hound states 181
10.2. How to produce and exploit unlimited promiscuous entanglement? 181
Chapter 11. Efficient production of pure N-mode Gaussian states 183
11.1. Degrees of freedom of pure Gaussian states: practical perspectives 183
11.2. Generic entanglement, standard form and state engineering of
block-diagonal pure Gaussian states 185
11.2.1. Generic entanglement of Gaussian states 185
11.2.2. Minimal number of parameters 185
11.2.3. Quantum state engineering 187
11.2.4. Standard forms: generic-entangled ↔ block-diagonal 189
11.3. Economical state engineering of arbitrary pure Gaussian states? 190
11.4. Generic versus typical entanglement: are off-block-diagonal correlations
relevant? 192
Part V Operational interpretation and applications of Gaussian
entanglement 193
Chapter 12. Multiparty quantum communication with Gaussian resources 195
12.1. Quantum teleportation with continuous variables 195
12.2. Equivalence between entanglement in symmetric Gaussian resource
states and optimal nonclassical teleportation fidelity 197
12.2.1. Optimal fidelity of two-party teleportation and bipartite
entanglement 198
12.2.2. Optimal fidelity of N-party teleportation networks and multipartite
entanglement 200
12.2.2.1. Entanglement of teleportation and localizable entanglement 204
12.2.3. Operational interpretation of tripartite Gaussian entanglement and
how to experimentally investigate its sharing structure 206
12.2.3.1. Entanglement of teleportation and residual contangle 206
12.2.3.2. The power of promiscuity in symmetric three-mode resources 206
12.2.3.3. Testing the promiscuous sharing of tripartite entanglement 207
12.2.4. Degradation of teleportation efficiency under quantum noise 209
12.2.5. Entanglement and optimal fidelity for nonsymmetric Gaussian
resources? 211
12.3. 1 ➝ 2 telecloning with bisymmetric and nonsymmetric three-mode
resources 211
12.3.1. Continuous variable “cloning at a distance” 211
12.3.2. Symmetric telecloning 212
12.3.2.1. Entanglement and teleportation fidelity are inequivalent for
nonsymmetric resources 214
12.3.3. Asymmetric telecloning 215