ScholarlyWiki - User contributions [en]

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[[File:CT-logo.png|150px|right|link=Quantum Collection Index]]
[[File:Quantum gravity combination.png|Quantum gravity|thumb|230px]]<br><br><br>
=<pre>Collection of Physics:Quantum Book I</pre>=
<div style="text-align:center;"> [[File:1-String Theory.jpg|40px|link=Book:Quantum Collection/Gallery]]<br> [[Book:Quantum Collection/Gallery|Gallery]] </div>
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}


=References=
{{reflist|3}}
==Further reading==

{{Author|Harold Foppele}}
= License of the Book=
{{imbox | text = Copyright ? 2026 H. Foppele and contributors. All rights reserved.}} [[Category:HandWiki encyclopedias]]

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<includeonly>
== Index ==

'''Core theory'''
[[Foundations]]
[[Conceptual and interpretations]]
[[Mathematical structure and systems]]
[[Atomic and spectroscopy]]
[[Wavefunctions and modes]]
[[Quantum dynamics and evolution]]
[[Measurement and information]]
[[Quantum information and computing]]

'''Applications and extensions'''
[[Quantum optics and experiments]]
[[Open quantum systems]]
[[Quantum field theory]]
[[Statistical mechanics and kinetic theory]]
[[Condensed matter and solid-state physics]]
[[Plasma and fusion physics]]
[[Timeline]]
[[Advanced and frontier topics]]

'''Quantum Book II'''
<li>[[Book:Quantum Collection/Matter (by scale)|Matter by scale]]</li>

'''Quantum Book III'''
<li>[[Book:Quantum Collection/Methods and tools|Methods and tools]]</li>

'''Quantum Book IV'''
<li>[[Book:Quantum Collection/Data Analysis Techniques in Particle Physics|Data Analysis Techniques]]</li>
== Full contents ==
<div class="mw-collapsible mw-collapsed" style="clear:both; border:1px solid #c8ccd1; background:#f8f9fa; padding:0.6em; margin:0.5em 0 1em 0;">

<ol>
=== Foundations ===
[[File:Quantum_operator_observable_yellow.jpg|thumb|250px|right]]
<li>[[Physics:Quantum basics]]</li>
<li>[[Physics:Quantum photoelectric effect]]</li>
<li>[[Physics:Quantum black-body radiation]]</li>
<li>[[Physics:Quantum Planck constant]]</li>
<li>[[Physics:Quantum Postulates]]</li>
<li>[[Physics:Quantum Hilbert space]]</li>
<li>[[Physics:Quantum Observables and operators]]</li>
<li>[[Physics:Quantum mechanics]]</li>
<li>[[Physics:Quantum mechanics measurements]]</li>
<li>[[Physics:Quantum state]]</li>
<li>[[Physics:Quantum system]]</li>
<li>[[Physics:Quantum superposition]]</li>
<li>[[Physics:Quantum probability]]</li>
<li>[[Physics:Quantum Mathematical Foundations of Quantum Theory]]</li>

=== Conceptual and interpretations ===
[[File:Interpretations of Quantum Mechanics2.jpg|thumb|250px|right]]
<li>[[Physics:Quantum Interpretations of quantum mechanics]]</li>
<li>[[Physics:Quantum Wave–particle duality]]</li>
<li>[[Physics:Quantum Complementarity principle]]</li>
<li>[[Physics:Quantum Uncertainty principle]]</li>
<li>[[Physics:Quantum Measurement problem]]</li>
<li>[[Physics:Quantum Bell's theorem]]</li>
<li>[[Physics:Quantum Hidden variable theory]]</li>
<li>[[Physics:Quantum nonlocality]]</li>
<li>[[Physics:Quantum contextuality]]</li>
<li>[[Physics:Quantum Darwinism]]</li>
<li>[[Physics:Quantum A Spooky Action at a Distance]]</li>
<li>[[Physics:Quantum A Walk Through the Universe]]</li>
<li>[[Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together]]</li>
<li>[[Physics:Quantum measurement problem]]</li>

=== Mathematical structure and systems ===
[[File:Scale of the universe.jpg|right|250px]]
<li>[[Physics:Quantum Density matrix]]</li>
<li>[[Physics:Quantum Exactly solvable quantum systems]]</li>
<li>[[Physics:Quantum many-body problem]]</li>
<li>[[Physics:Quantum Formulas Collection]]</li>
<li>[[Physics:Quantum A Matter Of Size]]</li>
<li>[[Physics:Quantum Symmetry in quantum mechanics]]</li>
<li>[[Physics:Quantum Noether theorem]]</li>
<li>[[Physics:Quantum Angular momentum operator]]</li>
<li>[[Physics:Quantum Runge–Lenz vector]]</li>
<li>[[Physics:Quantum Approximation Methods]]</li>
<li>[[Physics:Quantum Matter Elements and Particles]]</li>
<li>[[Physics:Quantum Dirac equation]]</li>
<li>[[Physics:Quantum Klein–Gordon equation]]</li>
<li>[[Physics:Quantum pendulum]]</li>
<li>[[Physics:Quantum configuration space]]</li>

=== Atomic and spectroscopy ===
[[File:Quantum Atomic Structure & Spectroscopy1.jpg|250px|right|Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.]]
<li>[[Physics:Quantum Atomic structure and spectroscopy]]</li>
<li>[[Physics:Quantum Hydrogen atom]]</li>
<li>[[Physics:Quantum number]]</li>
<li>[[Physics:Quantum Multi-electron atoms]]</li>
<li>[[Physics:Quantum Fine structure]]</li>
<li>[[Physics:Quantum Hyperfine structure]]</li>
<li>[[Physics:Quantum Isotopic shift]]</li>
<li>[[Physics:Quantum defect]]</li>
<li>[[Physics:Quantum Zeeman effect]]</li>
<li>[[Physics:Quantum Stark effect]]</li>
<li>[[Physics:Quantum Spectral lines and series]]</li>
<li>[[Physics:Quantum Selection rules]]</li>
<li>[[Physics:Quantum Fermi's golden rule]]</li>
<li>[[Physics:Quantum beats]]</li>

=== Wavefunctions and modes ===
[[File:Quantum_wavefunction.svg|250px|right|A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.]]
<li>[[Physics:Quantum Wavefunction]]</li>
<li>[[Physics:Quantum Superposition principle]]</li>
<li>[[Physics:Quantum Eigenstates and eigenvalues]]</li>
<li>[[Physics:Quantum Boundary conditions and quantization]]</li>
<li>[[Physics:Quantum Standing waves and modes]]</li>
<li>[[Physics:Quantum Normal modes and field quantization]]</li>
<li>[[Physics:Number of independent spatial modes in a spherical volume]]</li>
<li>[[Physics:Quantum Density of states]]</li>
<li>[[Physics:Quantum carpet]]</li>

=== Quantum dynamics and evolution ===
[[File:Quantum_time_evolution.jpg|250px|right]]
<li>[[Physics:Quantum Time evolution]]</li>
<li>[[Physics:Quantum Schrödinger equation]]</li>
<li>[[Physics:Quantum Time-dependent Schrödinger equation]]</li>
<li>[[Physics:Quantum Stationary states]]</li>
<li>[[Physics:Quantum Perturbation theory]]</li>
<li>[[Physics:Quantum Time-dependent perturbation theory]]</li>
<li>[[Physics:Quantum Adiabatic theorem]]</li>
<li>[[Physics:Quantum Berry phase]]</li>
<li>[[Physics:Quantum Aharonov-Bohm effect]]</li>
<li>[[Physics:Quantum Aharonov-Casher effect]]</li>
<li>[[Physics:Quantum Scattering theory]]</li>
<li>[[Physics:Quantum Scattering matrix]]</li>
<li>[[Physics:Quantum S-matrix]]</li>
<li>[[Physics:Quantum tunnelling]]</li>
<li>[[Physics:Quantum speed limit]]</li>
<li>[[Physics:Quantum revival]]</li>
<li>[[Physics:Quantum reflection]]</li>
<li>[[Physics:Quantum oscillations]]</li>
<li>[[Physics:Quantum jump]]</li>
<li>[[Physics:Quantum boomerang effect]]</li>
<li>[[Physics:Quantum chaos]]</li>

=== Measurement and information ===
[[File:Quantum_measurement_problem.jpg|250px|right]]
<li>[[Physics:Quantum Measurement theory]]</li>
<li>[[Physics:Quantum Measurement operators]]</li>
<li>[[Physics:Quantum Projective measurement]]</li>
<li>[[Physics:Quantum POVM]]</li>
<li>[[Physics:Quantum Weak measurement]]</li>
<li>[[Physics:Quantum Measurement collapse]]</li>
<li>[[Physics:Quantum entanglement]]</li>
<li>[[Physics:Quantum Zeno effect]]</li>
<li>[[Physics:Quantum limit]]</li>

=== Quantum information and computing ===
[[File:Quantum_information_theory_yellow.jpg|250px|right]]
<li>[[Physics:Quantum information theory]]</li>
<li>[[Physics:Quantum Qubit]]</li>
<li>[[Physics:Quantum Entanglement]]</li>
<li>[[Physics:Quantum Bell state]]</li>
<li>[[Physics:Quantum Gates and circuits]]</li>
<li>[[Physics:Quantum BB84]]</li>
<li>[[Physics:Quantum No-cloning theorem]]</li>
<li>[[Physics:Quantum Computing Algorithms in the NISQ Era]]</li>
<li>[[Physics:Quantum Noisy Qubits]]</li>
<li>[[Physics:Quantum Boson sampling]]</li>
<li>[[Physics:Quantum random access code]]</li>
<li>[[Physics:Quantum pseudo-telepathy]]</li>
<li>[[Physics:Quantum network]]</li>
<li>[[Physics:Quantum money]]</li>
=== Quantum optics and experiments ===
[[File:Experimental_quantum_physics_yellow.jpg|250px|right|Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.]]
<li>[[Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy]]</li>
<li>[[Physics:Quantum Stern-Gerlach experiment]]</li>
<li>[[Physics:Quantum Experimental quantum physics]]</li>
<li>[[Physics:Quantum optics]]</li>
<li>[[Physics:Quantum optics beam splitter experiments]]</li>
<li>[[Physics:Quantum Mach-Zehnder interferometer]]</li>
<li>[[Physics:Quantum Hong-Ou-Mandel effect]]</li>
<li>[[Physics:Quantum eraser experiment]]</li>
<li>[[Physics:Quantum delayed-choice quantum eraser]]</li>
<li>[[Physics:Quantum Ultra fast lasers]]</li>
<li>[[Template:Quantum optics operators]]</li>
=== Open quantum systems ===
[[File:Open_quantum_systems_yellow.jpg|250px|right]]
<li>[[Physics:Quantum Open systems]]</li>
<li>[[Physics:Quantum Master equation]]</li>
<li>[[Physics:Quantum Lindblad equation]]</li>
<li>[[Physics:Quantum Decoherence]]</li>
<li>[[Physics:Quantum dissipation]]</li>
<li>[[Physics:Quantum Markov semigroup]]</li>
<li>[[Physics:Quantum Markovian dynamics]]</li>
<li>[[Physics:Quantum Non-Markovian dynamics]]</li>
<li>[[Physics:Quantum Trajectories]]</li>

=== Quantum field theory ===
[[File:Quantum book1 field theory qft basics yellow.png|250px|right|Quantum field theory: fields, particles, interactions, diagrams, and renormalization.]]
<li>[[Physics:Quantum field theory (QFT) basics]]</li>
<li>[[Physics:Quantum field theory (QFT) core]]</li>
<li>[[Physics:Quantum Fields and Particles]]</li>
<li>[[Physics:Quantum Second quantization]]</li>
<li>[[Physics:Quantum Fock space]]</li>
<li>[[Physics:Quantum Harmonic Oscillator field modes]]</li>
<li>[[Physics:Quantum Creation and annihilation operators]]</li>
<li>[[Physics:Quantum vacuum fluctuations]]</li>
<li>[[Physics:Quantum Casimir effect]]</li>
<li>[[Physics:Quantum Propagators in quantum field theory]]</li>
<li>[[Physics:Quantum Feynman diagrams]]</li>
<li>[[Physics:Quantum Path integral formulation]]</li>
<li>[[Physics:Quantum Renormalization in field theory]]</li>
<li>[[Physics:Quantum Renormalization group]]</li>
<li>[[Physics:Quantum Field Theory Gauge symmetry]]</li>
<li>[[Physics:Quantum Spontaneous symmetry breaking]]</li>
<li>[[Physics:Quantum Non-Abelian gauge theory]]</li>
<li>[[Physics:Quantum Electrodynamics (QED)]]</li>
<li>[[Physics:Quantum chromodynamics (QCD)]]</li>
<li>[[Physics:Quantum Electroweak theory]]</li>
<li>[[Physics:Quantum Standard Model]]</li>
<li>[[Physics:Quantum triviality]]</li>
<li>[[Physics:Quantum confinement problem]]</li>

=== Statistical mechanics and kinetic theory ===
[[File:Statistics distribution yellow.jpg|250px|right|Statistical mechanics and kinetic theory: distributions, ensembles, transport, and thermalization.]]
<li>[[Physics:Quantum Statistical mechanics]]</li>
<li>[[Physics:Quantum Partition function]]</li>
<li>[[Physics:Quantum Distribution functions]]</li>
<li>[[Physics:Quantum Liouville equation]]</li>
<li>[[Physics:Quantum Kinetic theory]]</li>
<li>[[Physics:Quantum Boltzmann equation]]</li>
<li>[[Physics:Quantum BBGKY hierarchy]]</li>
<li>[[Physics:Quantum Relaxation and thermalization]]</li>
<li>[[Physics:Quantum Thermodynamics]]</li>

=== Condensed matter and solid-state physics ===
[[File:Solid_state_band_structure.png|250px|right]]
<li>[[Physics:Quantum Band structure]]</li>
<li>[[Physics:Quantum Fermi surfaces]]</li>
<li>[[Physics:Quantum Landau levels]]</li>
<li>[[Physics:Quantum Semiconductor physics]]</li>
<li>[[Physics:Quantum Phonons]]</li>
<li>[[Physics:Quantum Electron-phonon interaction]]</li>
<li>[[Physics:Quantum Exchange interaction]]</li>
<li>[[Physics:Quantum Superconductivity]]</li>
<li>[[Physics:Quantum Topological phases of matter]]</li>
<li>[[Physics:Quantum well]]</li>
<li>[[Physics:Quantum spin liquid]]</li>
<li>[[Physics:Quantum spin Hall effect]]</li>
<li>[[Physics:Quantum phase transition]]</li>
<li>[[Physics:Quantum critical point]]</li>
<li>[[Physics:Quantum dot]]</li>

=== Plasma and fusion physics ===
[[File:Quantum methods magnetohydrodynamics yellow.png|250px|right|Plasma and fusion physics: magnetic confinement, plasma flow, turbulence, and collective field dynamics.]]
<li>[[Physics:Quantum Fusion reactions and Lawson criterion]]</li>
<li>[[Physics:Quantum Plasma (fusion context)]]</li>
<li>[[Physics:Quantum Magnetic confinement fusion]]</li>
<li>[[Physics:Quantum Inertial confinement fusion]]</li>
<li>[[Physics:Quantum Plasma instabilities and turbulence]]</li>
<li>[[Physics:Quantum Tokamak core plasma]]</li>
<li>[[Physics:Quantum Tokamak edge physics and recycling asymmetries]]</li>
<li>[[Physics:Quantum Stellarator]]</li>

=== Timeline ===
[[File:Quantum mechanics Timeview.jpg|right|250px]]
<li>[[Physics:Quantum mechanics/Timeline]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Pre-quantum era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Old quantum theory]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Modern quantum mechanics]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum field theory era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum information era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum technology era]]</li>
<li>[[Physics:Quantum_mechanics/Timeline/Quiz|Physics:Quantum mechanics/Timeline/Quiz]]</li>

=== Advanced and frontier topics ===
[[File:Black_hole_thermodynamics yellow.jpg|right|250px]]
<li>[[Physics:Quantum topology]]</li>
<li>[[Physics:Quantum battery]]</li>
<li>[[Physics:Quantum Supersymmetry]]</li>
<li>[[Physics:Quantum Black hole thermodynamics]]</li>
<li>[[Physics:Quantum Holographic principle]]</li>
<li>[[Physics:Quantum gravity]]</li>
<li>[[Physics:Quantum De Sitter invariant special relativity]]</li>
<li>[[Physics:Quantum Doubly special relativity]]</li>
<li>[[Physics:Quantum arithmetic geometry]]</li>
<li>[[Physics:Quantum unsolved problems]]</li>
<li>[[Physics:Quantum Yang-Mills mass gap]]</li>
<li>[[Physics:Quantum gravity problem]]</li>
<li>[[Physics:Quantum black hole information paradox]]</li>
<li>[[Physics:Quantum dark matter problem]]</li>
<li>[[Physics:Quantum neutrino mass problem]]</li>
<li>[[Physics:Quantum matter-antimatter asymmetry problem]]</li>

</ol>
</div>
</includeonly>

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{{Short description|Quantum eraser experiment with delayed measurement choices}}

{{ScholarlyWiki page top
|backlink={{Quantum book backlink|Quantum optics and experiments}}
{{Quantum article nav|previous=Physics:Quantum eraser experiment|previous label=Quantum eraser experiment|next=Physics:Quantum Ultra fast lasers|next label=Ultra fast lasers}}
|image=[[File:Quantum_Delayed_choice_quantum_eraser_educational_yellow.png|430px|Delayed-choice quantum eraser: interference and which-path information depend on the measurement context.]]
|text='''Quantum delayed-choice quantum eraser''' is a planned ScholarlyWiki page in the Quantum Collection about delayed-choice quantum eraser experiments.
}}

== Overview ==
Placeholder: explain how delayed measurement choices can sort events into interference and non-interference patterns without changing past events.

== Key ideas ==
Placeholder: cover entangled photons, which-path information, interference, coincidence counting, delayed measurement.

== Experimental idea ==
Placeholder: develop this section with definitions, experimental details, formulas, and links to related Quantum Collection pages.

== Which-path information ==
Placeholder: develop this section with definitions, experimental details, formulas, and links to related Quantum Collection pages.

== Coincidence patterns ==
Placeholder: develop this section with definitions, experimental details, formulas, and links to related Quantum Collection pages.

== Interpretation ==
Placeholder: develop this section with definitions, experimental details, formulas, and links to related Quantum Collection pages.

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum delayed-choice quantum eraser|1}}

Script

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{{Short description|Principle that an unknown quantum state cannot be copied perfectly}}

{{ScholarlyWiki page top
|backlink={{Quantum book backlink|Quantum information and computing}}
{{Quantum article nav|previous=Physics:Quantum BB84|previous label=BB84|next=Physics:Quantum Computing Algorithms in the NISQ Era|next label=Computing Algorithms in the NISQ Era}}
|image=[[File:Quantum_No_cloning_theorem_educational_yellow.png|430px|The no-cloning theorem: an unknown quantum state cannot be copied perfectly by a physical operation.]]
|text='''Quantum No-cloning theorem''' is a planned ScholarlyWiki page in the Quantum Collection about the no-cloning theorem in quantum information.
}}

== Overview ==
Placeholder: explain why linear quantum evolution forbids perfect copying of an arbitrary unknown quantum state.

== Key ideas ==
Placeholder: cover linearity, unknown states, quantum copying limits, cryptography, measurement disturbance.

== Statement of the theorem ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Simple linearity argument ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Consequences for cryptography ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Relation to measurement ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum No-cloning theorem|1}}

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{{Short description|Photonic sampling model for quantum advantage studies}}

{{ScholarlyWiki page top
|backlink={{Quantum book backlink|Quantum information and computing}}
{{Quantum article nav|previous=Physics:Quantum Noisy Qubits|previous label=Noisy Qubits|next=Physics:Quantum random access code|next label=Random access code}}
|image=[[File:Quantum_Boson_sampling_educational_yellow.png|430px|Boson sampling with photons passing through a multiport interferometer and sampled at detectors.]]
|text='''Quantum Boson sampling''' is a planned ScholarlyWiki page in the Quantum Collection about boson sampling and photonic quantum computation.
}}

== Overview ==
Placeholder: describe boson sampling as a restricted photonic model in which identical photons pass through a linear optical network and produce output samples.

== Key ideas ==
Placeholder: cover indistinguishable photons, linear optics, interferometers, output distributions, quantum advantage.

== Linear optical network ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Sampling task ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Computational significance ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Experimental considerations ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Boson sampling|1}}

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{{Short description|Maximally entangled two-qubit quantum state}}

{{ScholarlyWiki page top
|backlink={{Quantum book backlink|Quantum information and computing}}
{{Quantum article nav|previous=Physics:Quantum Entanglement|previous label=Entanglement|next=Physics:Quantum Gates and circuits|next label=Gates and circuits}}
|image=[[File:Quantum_Bell_state_educational_yellow.png|430px|Bell states as correlated two-qubit entangled states used in quantum information.]]
|text='''Quantum Bell state''' is a planned ScholarlyWiki page in the Quantum Collection about Bell states and two-qubit entanglement.
}}

== Overview ==
Placeholder: introduce Bell states as maximally entangled two-qubit states and explain why they are central in quantum information.

== Key ideas ==
Placeholder: cover entanglement, two-qubit correlations, Bell basis, quantum teleportation, superdense coding.

== Bell basis ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Correlations ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Preparation in circuits ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Uses in protocols ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Bell state|1}}

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2026-05-21T22:19:09Z

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{{Short description|Quantum key distribution protocol using non-orthogonal bases}}

{{ScholarlyWiki page top
|backlink={{Quantum book backlink|Quantum information and computing}}
{{Quantum article nav|previous=Physics:Quantum Gates and circuits|previous label=Gates and circuits|next=Physics:Quantum No-cloning theorem|next label=No-cloning theorem}}
|image=[[File:Quantum_BB84_educational_yellow.png|430px|BB84 quantum key distribution: basis choices, photon transmission, and eavesdropping checks.]]
|text='''Quantum BB84''' is a planned ScholarlyWiki page in the Quantum Collection about the BB84 quantum key distribution protocol.
}}

== Overview ==
Placeholder: explain how Alice and Bob use non-orthogonal polarization or spin bases to establish a shared secret key and detect eavesdropping.

== Key ideas ==
Placeholder: cover basis choice, quantum measurement disturbance, sifted keys, error checking, privacy amplification.

== Protocol idea ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Quantum states and bases ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Eavesdropping and error rates ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== Security role in quantum information ==
Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum BB84|1}}

Script

2026-05-21T22:14:55Z

Maintenance: Add

<includeonly>
== Index ==

'''Core theory'''
[[Foundations]]
[[Conceptual and interpretations]]
[[Mathematical structure and systems]]
[[Atomic and spectroscopy]]
[[Wavefunctions and modes]]
[[Quantum dynamics and evolution]]
[[Measurement and information]]
[[Quantum information and computing]]

'''Applications and extensions'''
[[Quantum optics and experiments]]
[[Open quantum systems]]
[[Quantum field theory]]
[[Statistical mechanics and kinetic theory]]
[[Condensed matter and solid-state physics]]
[[Plasma and fusion physics]]
[[Timeline]]
[[Advanced and frontier topics]]

'''Quantum Book II'''
<li>[[Book:Quantum Collection/Matter (by scale)|Matter by scale]]</li>

'''Quantum Book III'''
<li>[[Book:Quantum Collection/Methods and tools|Methods and tools]]</li>

'''Quantum Book IV'''
<li>[[Book:Quantum Collection/Data Analysis Techniques in Particle Physics|Data Analysis Techniques]]</li>
== Full contents ==
<div class="mw-collapsible mw-collapsed" style="clear:both; border:1px solid #c8ccd1; background:#f8f9fa; padding:0.6em; margin:0.5em 0 1em 0;">

<ol>
=== Foundations ===
[[File:Quantum_operator_observable_yellow.jpg|thumb|250px|right]]
<li>[[Physics:Quantum basics]]</li>
<li>[[Physics:Quantum photoelectric effect]]</li>
<li>[[Physics:Quantum black-body radiation]]</li>
<li>[[Physics:Quantum Planck constant]]</li>
<li>[[Physics:Quantum Postulates]]</li>
<li>[[Physics:Quantum Hilbert space]]</li>
<li>[[Physics:Quantum Observables and operators]]</li>
<li>[[Physics:Quantum mechanics]]</li>
<li>[[Physics:Quantum mechanics measurements]]</li>
<li>[[Physics:Quantum state]]</li>
<li>[[Physics:Quantum system]]</li>
<li>[[Physics:Quantum superposition]]</li>
<li>[[Physics:Quantum probability]]</li>
<li>[[Physics:Quantum Mathematical Foundations of Quantum Theory]]</li>

=== Conceptual and interpretations ===
[[File:Interpretations of Quantum Mechanics2.jpg|thumb|250px|right]]
<li>[[Physics:Quantum Interpretations of quantum mechanics]]</li>
<li>[[Physics:Quantum Wave–particle duality]]</li>
<li>[[Physics:Quantum Complementarity principle]]</li>
<li>[[Physics:Quantum Uncertainty principle]]</li>
<li>[[Physics:Quantum Measurement problem]]</li>
<li>[[Physics:Quantum Bell's theorem]]</li>
<li>[[Physics:Quantum Hidden variable theory]]</li>
<li>[[Physics:Quantum nonlocality]]</li>
<li>[[Physics:Quantum contextuality]]</li>
<li>[[Physics:Quantum Darwinism]]</li>
<li>[[Physics:Quantum A Spooky Action at a Distance]]</li>
<li>[[Physics:Quantum A Walk Through the Universe]]</li>
<li>[[Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together]]</li>
<li>[[Physics:Quantum measurement problem]]</li>

=== Mathematical structure and systems ===
[[File:Scale of the universe.jpg|right|250px]]
<li>[[Physics:Quantum Density matrix]]</li>
<li>[[Physics:Quantum Exactly solvable quantum systems]]</li>
<li>[[Physics:Quantum many-body problem]]</li>
<li>[[Physics:Quantum Formulas Collection]]</li>
<li>[[Physics:Quantum A Matter Of Size]]</li>
<li>[[Physics:Quantum Symmetry in quantum mechanics]]</li>
<li>[[Physics:Quantum Noether theorem]]</li>
<li>[[Physics:Quantum Angular momentum operator]]</li>
<li>[[Physics:Quantum Runge–Lenz vector]]</li>
<li>[[Physics:Quantum Approximation Methods]]</li>
<li>[[Physics:Quantum Matter Elements and Particles]]</li>
<li>[[Physics:Quantum Dirac equation]]</li>
<li>[[Physics:Quantum Klein–Gordon equation]]</li>
<li>[[Physics:Quantum pendulum]]</li>
<li>[[Physics:Quantum configuration space]]</li>

=== Atomic and spectroscopy ===
[[File:Quantum Atomic Structure & Spectroscopy1.jpg|250px|right|Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.]]
<li>[[Physics:Quantum Atomic structure and spectroscopy]]</li>
<li>[[Physics:Quantum Hydrogen atom]]</li>
<li>[[Physics:Quantum number]]</li>
<li>[[Physics:Quantum Multi-electron atoms]]</li>
<li>[[Physics:Quantum Fine structure]]</li>
<li>[[Physics:Quantum Hyperfine structure]]</li>
<li>[[Physics:Quantum Isotopic shift]]</li>
<li>[[Physics:Quantum defect]]</li>
<li>[[Physics:Quantum Zeeman effect]]</li>
<li>[[Physics:Quantum Stark effect]]</li>
<li>[[Physics:Quantum Spectral lines and series]]</li>
<li>[[Physics:Quantum Selection rules]]</li>
<li>[[Physics:Quantum Fermi's golden rule]]</li>
<li>[[Physics:Quantum beats]]</li>

=== Wavefunctions and modes ===
[[File:Quantum_wavefunction.svg|250px|right|A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.]]
<li>[[Physics:Quantum Wavefunction]]</li>
<li>[[Physics:Quantum Superposition principle]]</li>
<li>[[Physics:Quantum Eigenstates and eigenvalues]]</li>
<li>[[Physics:Quantum Boundary conditions and quantization]]</li>
<li>[[Physics:Quantum Standing waves and modes]]</li>
<li>[[Physics:Quantum Normal modes and field quantization]]</li>
<li>[[Physics:Number of independent spatial modes in a spherical volume]]</li>
<li>[[Physics:Quantum Density of states]]</li>
<li>[[Physics:Quantum carpet]]</li>

=== Quantum dynamics and evolution ===
[[File:Quantum_time_evolution.jpg|250px|right]]
<li>[[Physics:Quantum Time evolution]]</li>
<li>[[Physics:Quantum Schrödinger equation]]</li>
<li>[[Physics:Quantum Time-dependent Schrödinger equation]]</li>
<li>[[Physics:Quantum Stationary states]]</li>
<li>[[Physics:Quantum Perturbation theory]]</li>
<li>[[Physics:Quantum Time-dependent perturbation theory]]</li>
<li>[[Physics:Quantum Adiabatic theorem]]</li>
<li>[[Physics:Quantum Berry phase]]</li>
<li>[[Physics:Quantum Aharonov-Bohm effect]]</li>
<li>[[Physics:Quantum Aharonov-Casher effect]]</li>
<li>[[Physics:Quantum Scattering theory]]</li>
<li>[[Physics:Quantum Scattering matrix]]</li>
<li>[[Physics:Quantum S-matrix]]</li>
<li>[[Physics:Quantum tunnelling]]</li>
<li>[[Physics:Quantum speed limit]]</li>
<li>[[Physics:Quantum revival]]</li>
<li>[[Physics:Quantum reflection]]</li>
<li>[[Physics:Quantum oscillations]]</li>
<li>[[Physics:Quantum jump]]</li>
<li>[[Physics:Quantum boomerang effect]]</li>
<li>[[Physics:Quantum chaos]]</li>

=== Measurement and information ===
[[File:Quantum_measurement_problem.jpg|250px|right]]
<li>[[Physics:Quantum Measurement theory]]</li>
<li>[[Physics:Quantum Measurement operators]]</li>
<li>[[Physics:Quantum Projective measurement]]</li>
<li>[[Physics:Quantum POVM]]</li>
<li>[[Physics:Quantum Weak measurement]]</li>
<li>[[Physics:Quantum Measurement collapse]]</li>
<li>[[Physics:Quantum entanglement]]</li>
<li>[[Physics:Quantum Zeno effect]]</li>
<li>[[Physics:Quantum limit]]</li>

=== Quantum information and computing ===
[[File:Quantum_information_theory_yellow.jpg|250px|right]]
<li>[[Physics:Quantum information theory]]</li>
<li>[[Physics:Quantum Qubit]]</li>
<li>[[Physics:Quantum Entanglement]]</li>
<li>[[Physics:Quantum Bell state]]</li>
<li>[[Physics:Quantum Gates and circuits]]</li>
<li>[[Physics:Quantum BB84]]</li>
<li>[[Physics:Quantum No-cloning theorem]]</li>
<li>[[Physics:Quantum Computing Algorithms in the NISQ Era]]</li>
<li>[[Physics:Quantum Noisy Qubits]]</li>
<li>[[Physics:Quantum Boson sampling]]</li>
<li>[[Physics:Quantum random access code]]</li>
<li>[[Physics:Quantum pseudo-telepathy]]</li>
<li>[[Physics:Quantum network]]</li>
<li>[[Physics:Quantum money]]</li>
=== Quantum optics and experiments ===
[[File:Experimental_quantum_physics_yellow.jpg|250px|right|Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.]]
<li>[[Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy]]</li>
<li>[[Physics:Quantum optics beam splitter experiments]]</li>
<li>[[Physics:Quantum Ultra fast lasers]]</li>
<li>[[Physics:Quantum Experimental quantum physics]]</li>
<li>[[Physics:Quantum optics]]</li>
<li>[[Template:Quantum optics operators]]</li>

=== Open quantum systems ===
[[File:Open_quantum_systems_yellow.jpg|250px|right]]
<li>[[Physics:Quantum Open systems]]</li>
<li>[[Physics:Quantum Master equation]]</li>
<li>[[Physics:Quantum Lindblad equation]]</li>
<li>[[Physics:Quantum Decoherence]]</li>
<li>[[Physics:Quantum dissipation]]</li>
<li>[[Physics:Quantum Markov semigroup]]</li>
<li>[[Physics:Quantum Markovian dynamics]]</li>
<li>[[Physics:Quantum Non-Markovian dynamics]]</li>
<li>[[Physics:Quantum Trajectories]]</li>

=== Quantum field theory ===
[[File:Quantum book1 field theory qft basics yellow.png|250px|right|Quantum field theory: fields, particles, interactions, diagrams, and renormalization.]]
<li>[[Physics:Quantum field theory (QFT) basics]]</li>
<li>[[Physics:Quantum field theory (QFT) core]]</li>
<li>[[Physics:Quantum Fields and Particles]]</li>
<li>[[Physics:Quantum Second quantization]]</li>
<li>[[Physics:Quantum Fock space]]</li>
<li>[[Physics:Quantum Harmonic Oscillator field modes]]</li>
<li>[[Physics:Quantum Creation and annihilation operators]]</li>
<li>[[Physics:Quantum vacuum fluctuations]]</li>
<li>[[Physics:Quantum Casimir effect]]</li>
<li>[[Physics:Quantum Propagators in quantum field theory]]</li>
<li>[[Physics:Quantum Feynman diagrams]]</li>
<li>[[Physics:Quantum Path integral formulation]]</li>
<li>[[Physics:Quantum Renormalization in field theory]]</li>
<li>[[Physics:Quantum Renormalization group]]</li>
<li>[[Physics:Quantum Field Theory Gauge symmetry]]</li>
<li>[[Physics:Quantum Spontaneous symmetry breaking]]</li>
<li>[[Physics:Quantum Non-Abelian gauge theory]]</li>
<li>[[Physics:Quantum Electrodynamics (QED)]]</li>
<li>[[Physics:Quantum chromodynamics (QCD)]]</li>
<li>[[Physics:Quantum Electroweak theory]]</li>
<li>[[Physics:Quantum Standard Model]]</li>
<li>[[Physics:Quantum triviality]]</li>
<li>[[Physics:Quantum confinement problem]]</li>

=== Statistical mechanics and kinetic theory ===
[[File:Statistics distribution yellow.jpg|250px|right|Statistical mechanics and kinetic theory: distributions, ensembles, transport, and thermalization.]]
<li>[[Physics:Quantum Statistical mechanics]]</li>
<li>[[Physics:Quantum Partition function]]</li>
<li>[[Physics:Quantum Distribution functions]]</li>
<li>[[Physics:Quantum Liouville equation]]</li>
<li>[[Physics:Quantum Kinetic theory]]</li>
<li>[[Physics:Quantum Boltzmann equation]]</li>
<li>[[Physics:Quantum BBGKY hierarchy]]</li>
<li>[[Physics:Quantum Relaxation and thermalization]]</li>
<li>[[Physics:Quantum Thermodynamics]]</li>

=== Condensed matter and solid-state physics ===
[[File:Solid_state_band_structure.png|250px|right]]
<li>[[Physics:Quantum Band structure]]</li>
<li>[[Physics:Quantum Fermi surfaces]]</li>
<li>[[Physics:Quantum Landau levels]]</li>
<li>[[Physics:Quantum Semiconductor physics]]</li>
<li>[[Physics:Quantum Phonons]]</li>
<li>[[Physics:Quantum Electron-phonon interaction]]</li>
<li>[[Physics:Quantum Exchange interaction]]</li>
<li>[[Physics:Quantum Superconductivity]]</li>
<li>[[Physics:Quantum Topological phases of matter]]</li>
<li>[[Physics:Quantum well]]</li>
<li>[[Physics:Quantum spin liquid]]</li>
<li>[[Physics:Quantum spin Hall effect]]</li>
<li>[[Physics:Quantum phase transition]]</li>
<li>[[Physics:Quantum critical point]]</li>
<li>[[Physics:Quantum dot]]</li>

=== Plasma and fusion physics ===
[[File:Quantum methods magnetohydrodynamics yellow.png|250px|right|Plasma and fusion physics: magnetic confinement, plasma flow, turbulence, and collective field dynamics.]]
<li>[[Physics:Quantum Fusion reactions and Lawson criterion]]</li>
<li>[[Physics:Quantum Plasma (fusion context)]]</li>
<li>[[Physics:Quantum Magnetic confinement fusion]]</li>
<li>[[Physics:Quantum Inertial confinement fusion]]</li>
<li>[[Physics:Quantum Plasma instabilities and turbulence]]</li>
<li>[[Physics:Quantum Tokamak core plasma]]</li>
<li>[[Physics:Quantum Tokamak edge physics and recycling asymmetries]]</li>
<li>[[Physics:Quantum Stellarator]]</li>

=== Timeline ===
[[File:Quantum mechanics Timeview.jpg|right|250px]]
<li>[[Physics:Quantum mechanics/Timeline]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Pre-quantum era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Old quantum theory]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Modern quantum mechanics]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum field theory era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum information era]]</li>
<li>[[Physics:Quantum mechanics/Timeline/Quantum technology era]]</li>
<li>[[Physics:Quantum_mechanics/Timeline/Quiz|Physics:Quantum mechanics/Timeline/Quiz]]</li>

=== Advanced and frontier topics ===
[[File:Black_hole_thermodynamics yellow.jpg|right|250px]]
<li>[[Physics:Quantum topology]]</li>
<li>[[Physics:Quantum battery]]</li>
<li>[[Physics:Quantum Supersymmetry]]</li>
<li>[[Physics:Quantum Black hole thermodynamics]]</li>
<li>[[Physics:Quantum Holographic principle]]</li>
<li>[[Physics:Quantum gravity]]</li>
<li>[[Physics:Quantum De Sitter invariant special relativity]]</li>
<li>[[Physics:Quantum Doubly special relativity]]</li>
<li>[[Physics:Quantum arithmetic geometry]]</li>
<li>[[Physics:Quantum unsolved problems]]</li>
<li>[[Physics:Quantum Yang-Mills mass gap]]</li>
<li>[[Physics:Quantum gravity problem]]</li>
<li>[[Physics:Quantum black hole information paradox]]</li>
<li>[[Physics:Quantum dark matter problem]]</li>
<li>[[Physics:Quantum neutrino mass problem]]</li>
<li>[[Physics:Quantum matter-antimatter asymmetry problem]]</li>

</ol>
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