Bibliographic Guide to Foundations of Quantum Mechanics - A. Cabello




Contains...
I. Hidden variables 4
A. Von Neumann’s impossibility proof 4
B. Einstein-Podolsky-Rosen’s argument of incompleteness of QM4
1. General 4
2. Bohr’s reply to EPR 4
C. Gleason theorem 4
D. Other proofs of impossibility of hidden variables5
E. Bell-Kochen-Specker theorem 5
1. The BKS theorem 5
2. From the BKS theorem to the BKS with locality theorem5
3. The BKS with locality theorem 5
4. Probabilistic versions of the BKS theorem5
5. The BKS theorem and the existence of dense “KS-colourable” subsets of projectors5
6. The BKS theorem in real experiments 6
F. Bell’s inequalities 6
1. First works 6
2. Bell’s inequalities for two spin-s particles6
3. Bell’s inequalities for two particles and more than two observables per particle6
4. Bell’s inequalities for n particles 6
5. Which states violate Bell’s inequalities?7
6. Other inequalities 7
7. Inequalities to detect genuine n-particle nonseparability7
8. Herbert’s proof of Bell’s theorem 7
9. Mermin’s statistical proof of Bell’s theorem7
G. Bell’s theorem without inequalities 7
1. Greenberger-Horne-Zeilinger’s proof 7
2. Peres’ proof of impossibility of recursive elements of reality7
3. Hardy’s proof 7
4. Bell’s theorem without inequalities for EPR-Bohm-Bell states8
5. Other algebraic proofs of no-local hidden variables8
6. Classical limits of no-local hidden variables proofs8
H. Other “nonlocalities” 8
1. “Nonlocality” of a single particle 8
2. Violations of local realism exhibited in sequences of measurements (“hidden nonlocality”)8
3. Local immeasurability or indistinguishability (“nonlocality without entanglement”)8
I. Experiments on Bell’s theorem 8
1. Real experiments 8
2. Proposed gedanken experiments 9
3. EPR with neutral kaons 9
4. Reviews 9
5. Experimental proposals on GHZ proof, preparation of
6. Experimental proposals on Hardy’s proof10
7. Some criticisms of the experiments on Bell’s inequalities.
II. “Interpretations” 10
A. Copenhagen interpretation 10
B. De Broglie’s “pilot wave” and Bohm’s “causal” interpretations
1. General 11
2. Tunneling times in Bohmian mechanics12
C. “Relative state”, “many worlds”, and “many minds” interpretations
D. Interpretations with explicit collapse or dynamical reduction
E. Statistical (or ensemble) interpretation 12
F. “Modal” interpretations 13
G. “It from bit” 13
H. “Consistent histories” (or “decoherent histories”)13
I. Decoherence and environment induced superselection13
J. Time symetric formalism, pre- and post-selected systems,
K. The transactional interpretation 14
L. The Ithaca interpretation: Correlations without correlata
III. Composite systems, preparations, and measurements14
A. States of composite systems 14
1. Schmidt decomposition 14
2. Entanglement measures 14
3. Separability criteria 15
4. Multiparticle entanglement 15
5. Entanglement swapping 15
6. Entanglement distillation (concentration and purification)
7. Disentanglement 16
8. Bound entanglement 16
9. Entanglement as a catalyst 16
B. State determination, state discrimination, and measuremen
1. State determination, quantum tomography16
2. Generalized measurements, positive operator-valued measuremen
3. State preparation and measurement of arbitrary observ
4. Stern-Gerlach experiment and its successors17
3
5. Bell operator measurements 18
IV. Quantum effects 18
6. Quantum Zeno and anti-Zeno effects 18
7. Reversible measurements, delayed choice and quantum erasure18
8. Quantum nondemolition measurements19
9. “Interaction-free” measurements 19
10. Other applications of entanglement 19
V. Quantum information 20
A. Quantum cryptography 20
1. General 20
2. Proofs of security 20
3. Quantum eavesdropping 21
4. Quantum key distribution with orthogonal states21
5. Experiments 21
6. Commercial quantum cryptography 21
B. Cloning and deleting quantum states 21
C. Quantum bit commitment 22
D. Secret sharing and quantum secret sharing 22
E. Quantum authentication 23
F. Teleportation of quantum states 23
1. General 23
2. Experiments 24
G. Telecloning 24
H. Dense coding 24
I. Remote state preparation and measurement24
J. Classical information capacity of quantum channels25
K. Quantum coding, quantum data compression25
L. Reducing the communication complexity with quantum entanglement25
M. Quantum games and quantum strategies 25
N. Quantum clock synchronization 26
VI. Quantum computation 26
A. General 26
B. Quantum algorithms 27
1. Deutsch-Jozsa’s and Simon’s 27
2. Factoring 27
3. Searching 27
4. Simulating quantum systems 28
5. Quantum random walks 28
6. General and others 28
C. Quantum logic gates 28
D. Schemes for reducing decoherence 28
E. Quantum error correction 29
F. Decoherence-free subspaces and subsystems29
G. Experiments and experimental proposals 29
VII. Miscellaneous 30
A. Textbooks 30
B. History of quantum mechanics 30


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