Do We Really Understand Quantum Mechanics?.

Laloë, Franck.
Cambridge : Cambridge University Press, 2012.
1 online resource (410 pages)

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Quantum theory.
Science -- Philosophy.
Electronic books.
Gives an overview of the quantum theory and its main interpretations. Ideal for researchers in physics and mathematics.
1 Historical perspective
1.1 Three periods
1.1.1 Prehistory
1.1.2 The undulatory period
1.1.3 Emergence of the Copenhagen interpretation
1.2 The state vector
1.2.1 Definition, Schrödinger evolution, Born rule
1.2.1.a Definition
1.2.1.b Schrödinger evolution
1.2.1.c Born probability rule
1.2.2 Measurement processes
1.2.2.a Von Neumann, reduction (collapse)
1.2.2.b Bohr
1.2.3 Status
1.2.3.a Two extremes
1.2.3.b The Copenhagen (orthodox) point of view
2 Present situation, remaining conceptual difficulties
2.1 Von Neumann's infinite regress/chain
2.2 Schrödinger's cat
2.2.1 The argument
2.2.2 Misconceptions
2.2.3 Modern cats
2.3 Wigner's friend
2.4 Negative and "interaction-free" measurements
2.5 A variety of points of view
Copenhagen interpretation:
Critics of the Copenhagen interpretation:
More recent comments:
Present situation:
2.6 Unconvincing arguments
3 The theorem of Einstein, Podolsky, and Rosen
3.1 A theorem
3.2 Of peas, pods, and genes
3.2.1 Simple experiments: no conclusion yet
3.2.2 Correlations: causes unveiled
3.2.2.a Same measurement parameters
3.2.2.b Different measurements parameters
3.2.2.c Summary
3.3 Transposition to physics
3.3.1 The EPR argument for two correlated microscopic particles
3.3.1.a Assumptions
3.3.1.b Conclusions
3.3.2 Bohr's reply
3.3.3 Locality and separability
3.3.3.a Various aspects of locality
3.3.3.b Quantum non-separability
3.3.4 The EPR argument for macroscopic systems
4 Bell theorem
4.1 Bell inequalities
4.1.1 Quantum mechanics: two spins in a singlet state
4.1.2 Local realism: proof of the BCHSH inequality.
4.1.3 Contradiction with quantum mechanics
4.1.4 Logical content
4.1.5 Contradiction with experiments
4.2 Various forms of the theorem
4.2.1 Other inequalities
4.2.1.a Bell 1964
4.2.1.b Wigner inequalities
4.2.1.c Mermin inequality
4.2.2 Other sets of assumptions
4.2.3 Generalizations of the theorem, role of locality
4.2.4 Status of the theorem
attempts to bypass it
4.3 Cirelson's theorem
4.3.1 Measurements on two-level sub-systems
4.3.2 Maximal quantum violation
4.4 No instantaneous signaling
4.4.1 Non-signaling (NS) conditions
4.4.2 Logical boxes
4.4.2.a Deterministic boxes
4.4.2.b Stochastic boxes
4.4.2.c Local stochastic boxes
4.4.3 Popescu-Rohrlich boxes
4.4.4 How to characterize quantum mechanics?
4.5 Impact of the theorem: where do we stand now?
4.5.1 Loopholes, conspiracies
4.5.1.a Pair selection loophole (efficiency loophole)
4.5.1.b Conspiracy (or communication) loophole
4.5.1.c Fatalism versus free will
4.5.1.d Credibility of loopholes
4.5.2 Is quantum mechanics itself non-local? Counterfactuality
5 More theorems
5.1 GHZ contradiction
5.1.1 Derivation
5.1.2 Discussion
5.2 Generalizing GHZ (all or nothing states)
5.3 Cabello's inequality
5.3.1 Local realist point of view
5.3.2 Contradiction with quantum mechanics
5.4 Hardy's impossibilities
5.5 Bell-Kochen-Specker theorem: contextuality
5.5.1 A spin 1 particle
5.5.2 Two spin 1/2 particles, product rule
5.5.3 Contextuality versus local realism
6 Quantum entanglement
6.1 A purely quantum property
6.1.1 The part and the whole
6.1.2 Two possible origins of correlations
6.2 Characterizing entanglement
6.2.1 Schmidt decomposition of a pure state
6.2.2 Statistical entropies
6.2.3 Measures of entanglement
6.2.4 Monogamy.
6.2.5 Separability criterion for density operators
6.3 Creating and losing entanglement
6.3.1 Entanglement created by local interactions
6.3.2 Entanglement swapping
6.3.3 Decoherence
6.3.3.a Mechanism
6.3.3.b Revisiting the Schrödinger cat
6.3.4 Purification, distillation
6.4 Quantum dynamics of a sub-system
6.4.1 Kraus operators
6.4.1.a A first calculation
6.4.1.b An upper limit of the number of Kraus operators
6.4.2 Density operator, Kraus sum
6.4.3 Master equation, Lindblad form
7 Applications of quantum entanglement
7.1 Two theorems
7.1.1 No-cloning
7.1.2 No single shot state determination
7.2 Quantum cryptography
7.2.1 Sharing cryptographic keys
7.2.2 Examples of protocols for key exchange
7.2.2.a BB84 protocol
7.2.2.b EPR protocol
7.3 Teleporting a quantum state
7.4 Quantum computation and information
7.4.1 General idea
7.4.2 Quantum gates and algorithms
7.4.3 Quantum error correction codes
8 Quantum measurement
8.1 Direct measurements
8.1.1 Ideal measurement, Von Neumann model
8.1.1.a Basic measurement process
8.1.1.b Effects of the interaction, pointer observable
8.1.2 Effects of the environment
8.1.2.a Ambiguous entanglement
8.1.2.b Pointer states
8.1.3 Hund paradox
8.2 Indirect measurements
8.2.1 A simple model: two-level system
8.2.1.a Interaction and entanglement
8.2.1.b Measurement on the ancillary system
8.2.2 Generalization: POVM
8.3 Weak and continuous measurements
8.3.1 Measurements of weak values
8.3.2 Continuous measurements
8.3.2.a Probability of the result
8.3.2.b Evolution of the state
8.3.2.c Wiener process: stochastic differential equation
9 Experiments: quantum reduction seen in real time
9.1 Single ion in a trap
9.2 Single electron in a trap.
9.3 Measuring the number of photons in a cavity
9.4 Spontaneous phase of Bose-Einstein condensates
9.4.1 Interferences between independent condensates
9.4.2 An additional variable?
9.4.3 Non-locality of phase
10 Various interpretations
10.1 Pragmatism in laboratories
10.1.1 Common sense: breaking the Von Neumann chain by hand
10.1.1.a Modified decoherence
10.1.1.b Effect of consciousness
10.1.2 Correlation interpretation
10.1.2.a Calculating the probability for a sequence of results in successive measurements
10.1.2.b Getting rid of state vector reduction
10.1.2.c Discussion
10.1.3 Emphasizing information
10.2 Statistical interpretation
10.3 Relational interpretation, relative state vector
10.3.1 Relational interpretation
10.3.2 Pure informational point of view
10.4 Logical, algebraic, and deductive approaches
10.4.1 Quantum logic
10.4.2 Algebraic theory
10.4.3 Formal axiomatic theory
10.4.4 Gleason theorem
10.5 Veiled reality
10.6 Additional ("hidden") variables
10.6.1 Bohmian theory
10.6.1.a General framework
Quantum equilibrium condition
Description of physical reality
10.6.1.b Bohmian trajectories
One particle
10.6.1.c Quantum measurement, non-locality
10.6.1.d Spin and field theory
Bohmian field theory
10.6.1.e Objections and solutions
Are Bohmian trajectories real?
Measurement and entanglement
Correlation between measurements at different times
The structures of the two theories are similar
10.6.1.f Summary and discussion
10.6.2 Nelson mechanics
10.7 Modal interpretation
10.8 Modified Schrödinger dynamics
10.8.1 Evolution of the ideas
10.8.1.a Early work
10.8.1.b Spontaneous localization ("hits")
10.8.1.c Continuous spontaneous localization
10.8.1.d Relation with gravity.
10.8.1.e Relation with relativity
10.8.1.f Relation with experiments
10.8.2 Physical description of reality within modified dynamics
10.8.3 Open quantum systems in standard quantum mechanics
10.9 Transactional interpretation
10.10 History interpretation
10.10.1 Histories, families of histories
10.10.2 Consistent families
10.10.3 Quantum evolution of an isolated system
10.10.4 Incompatibility of different consistent families
10.10.5 Comparison with other interpretations
10.10.6 A profusion of histories
10.11 Everett interpretation
10.11.1 No limit for the Schrödinger equation
10.11.2 Consistency of the interpretation
10.11.3 Discussion
10.12 Conclusion
11 Annex: Basic mathematical tools of quantum mechanics
11.1 General physical system
11.1.1 Quantum space of states
11.1.2 Operators
11.1.2.a Product, commutator, eigenvectors
11.1.2.b Hermitian and unitary operators
11.1.2.c Trace
11.1.3 Probabilities
11.1.4 Time evolution
11.1.5 Density operator
11.1.5.a Definition
11.1.5.b Pure states and statistical mixtures
11.1.5.c Time evolution
11.1.5.d Statistical entropy
11.1.6 Simple case, spin 1/2
11.2 Grouping several physical systems
11.2.1 Tensor product
11.2.2 Ensemble of spins 1/2
11.2.3 Partial traces
11.3 Particles in a potential
11.3.1 Single particle
11.3.1.a Wave function
11.3.2 Spin, Stern-Gerlach experiment
11.3.2.a Introduction of spin
11.3.2.b Space of states
11.3.3 Several particles
Appendix A: Mental content of the state vector
Appendix B: Bell inequalities in non-deterministic local theories
Appendix C: An attempt for constructing a "separable" quantum theory (non-deterministic but local)
Appendix D: Maximal probability for a state.
Appendix E: The influence of pair selection.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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Print version: Laloë, Franck Do We Really Understand Quantum Mechanics?