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Gauge symmetry cannot be spontaneously broken
In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing
Elitzur's_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
No spontaneous symmetry breaking in two-dimensional systems at finite temperature
Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous
Mermin–Wagner_theorem
Mechanism that explains the generation of mass for gauge bosons
symmetry breaking of a gauge symmetry is technically incorrect since by Elitzur's theorem gauge symmetries never can be spontaneously broken. Rather, the
Higgs_mechanism
Theorem in quantum mechanics
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from
Gleason's_theorem
Theorem in quantum mechanics
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position
Ehrenfest_theorem
Theorem in quantum mechanics
In quantum mechanics, the Hellmann–Feynman theorem relates the derivative of the total energy with respect to a parameter to the expectation value of
Hellmann–Feynman_theorem
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Symmetry breaking through the vacuum state
physics. The term "spontaneous symmetry breaking" is a misnomer here as Elitzur's theorem states that local gauge symmetries can never be spontaneously broken
Spontaneous_symmetry_breaking
Quantum mechanics thought experiment
The Elitzur–Vaidman bomb-tester is a quantum mechanics thought experiment that uses interaction-free measurements to verify that a bomb is functional
Elitzur–Vaidman_bomb_tester
Thermal Wilson loop
makes the loop gauge dependent for z ≠ 1 {\displaystyle z\neq 1} , by Elitzur's theorem non-zero expectation values of ⟨ Φ ⟩ {\displaystyle \langle \Phi \rangle
Polyakov_loop
Gauge field loop operator
structure and is a phenomenon independent of the matter content. Elitzur's theorem ensures that local non-gauge invariant operators cannot have a non-zero
Wilson_loop
Type of quantum mechanics theory
incomplete description of reality. John Stewart Bell in 1964, in his eponymous theorem proved that correlations between particles under any local hidden variable
Hidden-variable_theory
Class of theories in quantum mechanics
In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices
Superdeterminism
Historical critique of quantum mechanics
local hidden-variable theory. This second result became known as the Bell theorem. To understand the first result, consider the following toy hidden-variable
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Description of physical properties at the atomic and subatomic scale
sending signals faster than light, as demonstrated by the no-communication theorem. Another possibility opened by entanglement is testing for "hidden variables"
Quantum_mechanics
View of quantum mechanics
unitary transformation applied to the Hamiltonian and state vectors. Haag's theorem says that the interaction picture doesn't exist in the case of interacting
Interaction_picture
Interpretation of quantum mechanics
by a range of detailed Bell test experiments. A collection of related theorems, beginning with Bell's proof in 1964, show that quantum mechanics is incompatible
Local_hidden-variable_theory
Testable implication of local hidden-variable theories
Clauser–Horne–Shimony–Holt (CHSH) inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics
CHSH_inequality
Method of inferring the results of a computation without running a quantum computer
concepts of counterfactual definiteness, on a re-interpretation of the Elitzur–Vaidman bomb tester thought experiment, and making theoretical use of the
Counterfactual quantum computation
Counterfactual_quantum_computation
Foundational principle in quantum physics
Hardy's Theorem while the version by Bonami–Demange–Jaming covers the full strength of Hardy's Theorem. A different proof of Beurling's theorem based on
Uncertainty_principle
Physics phenomenon
Greenberger, M. Horne, and A. Zeilinger, "Going beyond Bell's Theorem," in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M
Quantum_entanglement
Experiments to test Bell's theorem in quantum mechanics
and electrons. The test empirically evaluates the implications of Bell's theorem. As of 2015[update], all Bell tests have found that the hypothesis of local
Bell_test
Quantum mechanics principle
electrons, and later extended to all fermions with his spin–statistics theorem of 1940. In the case of electrons in atoms, the exclusion principle can
Pauli_exclusion_principle
Formulation of quantum mechanics
the answer is a Gaussian spreading linearly in time is the central limit theorem, which can be interpreted as the first historical evaluation of a statistical
Path-integral_formulation
Conceptual conflict between general relativity and quantum mechanics
scale invariance generates a conserved Weyl current according to Noether's theorem. In scale-invariant cosmological models, this Weyl current naturally gives
Problem_of_time
Value for the flow of probability in quantum mechanics
} and the integral equation can also be restated using the divergence theorem as: ∂ ∂ t ∫ V | Ψ | 2 d V + {\displaystyle {\frac {\partial }{\partial
Probability_current
Force resulting from the quantisation of a field
Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman axioms Equations Dirac equation Klein–Gordon equation Proca equations
Casimir_effect
Cryptography based on quantum mechanical phenomena
properties such as quantum entanglement, measurement disturbance, no-cloning theorem, and the principle of superposition to perform encryption tasks. Quantum
Quantum_cryptography
Experimentally violated inequality of correlations of entangled particles
"Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem". Foundations of Physics. 33 (10): 1469–1493. Bibcode:2003FoPh...33.1469L
Leggett_inequality
Lowest possible energy of a quantum system or field
Callen and Theodore Welton proved the quantum fluctuation-dissipation theorem (FDT) which was originally formulated in classical form by Nyquist (1928)
Zero-point_energy
Interpretation of quantum mechanics
Bell's Theorem: The Changing Face of Nonlocality". In Mary Bell; Shan Gao (eds.). Quantum Nonlocality and Reality: 50 years of Bell's theorem. Cambridge
Many-worlds_interpretation
Quantum states of two qubits
faster than the speed of light, a result known as the no-communication theorem. The Bell states are four specific maximally entangled quantum states of
Bell_state
Interdisciplinary research area
key usability problem for quantum machine learning by providing rigorous theorems that predict whether a given architecture will remain trainable as it scales
Quantum_machine_learning
Concept in quantum entanglement
Adán Cabello [es] that developed simplifying demonstrations of Bell's theorem. The game has been reformulated to demonstrate quantum pseudo-telepathy
Quantum_pseudo-telepathy
Description of a quantum-mechanical system
satisfy the Ehrenfest theorem. For a one-dimensional quantum particle moving in a potential V {\displaystyle V} , the Ehrenfest theorem says m d d t ⟨ x ⟩
Schrödinger_equation
Formulation of quantum mechanics
P(t) satisfy the classical equations of motion; also see Ehrenfest's theorem, below. When it was introduced by Werner Heisenberg, Max Born and Pascual
Matrix_mechanics
Mathematical entity to describe the probability of each possible measurement on a system
Ground state Introduction to quantum mechanics No-cloning theorem Orthonormal basis PBR theorem Quantum harmonic oscillator Quantum logic gate Stationary
Quantum_state
Quantum error correcting code
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Calculation rule in quantum mechanics
the spectrum of A {\displaystyle A} is not wholly discrete, the spectral theorem proves the existence of a certain projection-valued measure (PVM) Q {\displaystyle
Born_rule
Interdisciplinary theory behind quantum computing
quantum entangled particle pairs, as the principles of the no-cloning theorem and wave function collapse ensure the secure exchange of the random keys
Quantum_information_science
Applications of machine learning to quantum physics
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Machine_learning_in_physics
Quantum mechanical model
Model for the potential energy of a diatomic molecule Bertrand's theorem – Physics theorem Mehler kernel – Complex-valued function Molecular vibration –
Quantum_harmonic_oscillator
Process by which a quantum system takes on a definitive state
from unknown values of hidden variables. Results from tests of Bell's theorem shows that these variables would need to be non-local. The second group
Wave_function_collapse
Hypothetical situation
(infinity) Hilbert's paradox of the Grand Hotel (infinity) Infinite monkey theorem (probability) Lottery paradox (probability) Sleeping beauty paradox (probability)
Thought_experiment
Interaction of a quantum system with a classical observer
information like a choice of basis for that vector to be embedded in. Gleason's theorem establishes the converse: all assignments of probabilities to unit vectors
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Formulation of quantum mechanics
context of quantum optics this equation is known as the optical equivalence theorem. (For details on the properties and interpretation of the Wigner function
Phase-space_formulation
Mathematical technique in physics
communication and found them all flawed and, consistent with the no-communication theorem, unable to transmit nonlocal signals. "In relativity, time and space are
Retrocausality
Deviations from local realism
the many-worlds interpretation which violates an assumption of Bell's theorem. Quantum nonlocality does not allow for faster-than-light communication
Quantum_nonlocality
Austrian quantum physicist (born 1945)
Horne to work on entanglement of more than two qubits. The resulting GHZ theorem (see Greenberger–Horne–Zeilinger state) is fundamental for quantum physics
Anton_Zeilinger
Quantum logic gate
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Cirac–Zoller controlled-NOT gate
Cirac–Zoller_controlled-NOT_gate
Concept in quantum mechanics
quantum physics the assumption of "local realism" must be abandoned. Bell's theorem proves that every type of quantum theory must necessarily violate locality
Counterfactual_definiteness
Relativistic quantum mechanical wave equation
equation more explicit, since they leave its action invariant. Noether's theorem then allows for the direct calculation of currents corresponding to these
Dirac_equation
of the 20th century, beginning with theoretical results like Holevo's theorem, the concept of generalized measurements or POVMs, the proposal of quantum
History_of_quantum_mechanics
Trapped-ion quantum gate
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Mølmer–Sørensen_gate
Mathematical tool in quantum physics
self-adjoint, and has trace one. Conversely, it follows from the spectral theorem that every operator with these properties can be written as ∑ j p j | ψ
Density_matrix
Mathematical structures that allow quantum mechanics to be explained
subsystem of a larger composite system in a pure state (see purification theorem). In the absence of quantum entanglement, the quantum state of the composite
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Interpretation of quantum mechanics
the NATO Advanced Research Workshop on Modality, Probability and Bell's Theorems, Kluwer, 233–255. Marchildon, L (2006). "Causal Loops and Collapse in the
Transactional_interpretation
Area of physical and philosophical debate
Journal of Physics. 69: 413–421. Bub, J.; Clifton, R. (1996). "A uniqueness theorem for interpretations of quantum mechanics". Studies in History and Philosophy
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
{A}}(t)}{\partial t}}} Time evolution in Heisenberg picture (Ehrenfest theorem) m = mass, V = potential energy, r = position, p = momentum, of a particle
List of equations in quantum mechanics
List_of_equations_in_quantum_mechanics
Quantum mechanical operator interchanging particle states as arguments to a function
particles satisfying the case of −1 are called fermions. The spin–statistics theorem dictates that all particles with integer spin are bosons whereas all particles
Exchange_operator
Means of studying the interaction of light and matter
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Circuit quantum electrodynamics
Circuit_quantum_electrodynamics
Fringe hypothesis
theory in 2013. Penrose's argument stemmed from Gödel's incompleteness theorems. In his first book on consciousness, The Emperor's New Mind (1989), he
Quantum_mind
Interpretation of quantum mechanics
between the probability density and the wave function has the status of a theorem, a result of a separate postulate, the "quantum equilibrium hypothesis"
De_Broglie–Bohm_theory
Statistical mechanics of quantum-mechanical systems
2007, p. 172. Kirkpatrick, K. A. (February 2006). "The Schrödinger-HJW Theorem". Foundations of Physics Letters. 19 (1): 95–102. arXiv:quant-ph/0305068
Quantum_statistical_mechanics
Quantum mechanical equation of motion of charged particles in magnetic field
{\textstyle \mathbf {J} =\mathbf {L} +\mathbf {S} } and Wigner-Eckart theorem. Thus we find [ | p | 2 2 m + μ B g J m j | B | − e ϕ ] | ψ ⟩ = i ℏ ∂ ∂
Pauli_equation
Notation for quantum states
functional, i.e. a ket with a bra, and vice versa (see Riesz representation theorem). The inner product on Hilbert space ( , ) {\displaystyle (\ ,\ )}
Bra–ket_notation
Mathematical description of quantum state
are essential for the statement and proof of many useful theorems, e.g. the spectral theorem. It is not very important in introductory quantum mechanics
Wave_function
Quantum mechanical phenomenon
modelled with the relativistic Dirac equation, well established mathematical theorems imply that the process is completely subluminal. It has also been proved
Quantum_tunnelling
Non-mathematical introduction
theory to converge to classical limits. A related concept is Ehrenfest's theorem, which shows that the average values obtained from quantum mechanics (e
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Theory of logic to account for observations from quantum theory
wavefunction collapse in the problem of quantum measurement, but Gleason's theorem presents severe difficulties for this goal. Later, Putnam retracted his
Quantum_logic
Quantum mechanical operator related to rotational symmetry
angular momentum. Total angular momentum is always conserved, see Noether's theorem. In quantum mechanics, angular momentum can refer to one of three different
Angular_momentum_operator
Optical device which splits a beam of light in two
{a}}_{d}^{\dagger }\right)^{m}|00\rangle _{cd}.} Using the multi-binomial theorem, this can be written | ψ out ⟩ = 1 n ! m ! ∑ j = 0 n ∑ k = 0 m ( n j )
Beam_splitter
Quantum mechanical statistic
pilot wave formulation, as not representing a basic law, but rather a theorem (called quantum equilibrium hypothesis) which applies when a quantum equilibrium
Quantum_potential
Formulation of quantum mechanics
automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger
Heisenberg_picture
Equation used in quantum scattering problems
and the process is assumed elastic. Now consider the Hellmann–Feynman theorem, which requires the energy eigenvalues of the Hamiltonian to change continuously
Lippmann–Schwinger_equation
Solution with prescribed norm
ISBN 978-0-8218-2783-3. Moser, J. (1960). "A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations"
Normalized solution (mathematics)
Normalized_solution_(mathematics)
Theoretical problem in quantum physics
Constructor theory Einstein's thought experiments EPR paradox Gleason's theorem Observer effect (physics) Observer (quantum physics) Philosophy of physics
Measurement_problem
Interpretation of quantum mechanics
states. (This is part of what would later be known as the Schrödinger–HJW theorem.) So, if pure states are supposed to represent objective uncertainty while
QBism
Mathematical inequality representing macroscopic objects
function Collapse Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Mach–Zehnder Delayed-choice quantum eraser Stern–Gerlach
Leggett–Garg_inequality
Quantum physics concept
starting with Hilbert spaces and unitary transformation, leading to the theorems of mutually unbiased bases. In the mathematical formulation of quantum
Complementarity_(physics)
Suitably normalized antisymmetrization of the phase-space star product
of commutators bypasses the negative result of the Groenewold–van Hove theorem, which precludes such an isomorphism for the Poisson bracket, a question
Moyal_bracket
Range of physical processes in physics
scattering Extinction Haag–Ruelle scattering theory Kikuchi line Levinson's theorem Light scattering by particles Linewidth Mie scattering Mie theory Molecular
Scattering
Study of the relations between thermodynamics and quantum mechanics
stated by Walther Nernst. The first formulation is known as the Nernst heat theorem, and can be phrased as: The entropy of any pure substance in thermodynamic
Quantum_thermodynamics
Physics Earl W. McDaniel Earle Hesse Kennard Earle M. Terry Earnshaw's theorem Earth's magnetic field Earth's shadow Earth, Moon, and Planets Earth-Moon
Index_of_physics_articles_(E)
Relativistic wave equation in quantum mechanics
calculating the currents associated with the symmetries using Noether's theorem. The equation can be derived analogously to how the Schrödinger equation
Klein–Gordon_equation
Quantum physics of light and matter in a cavity
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Cavity quantum electrodynamics
Cavity_quantum_electrodynamics
Superconducting qubit implementation
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Transmon
Converting classical mechanics to quantum mechanics
equivalence. Duck, Ian; Sudarshan, E C G (1998). Pauli and the Spin-Statistics Theorem. WORLD SCIENTIFIC. doi:10.1142/3457. ISBN 978-981-02-3114-9. Dirac, P.
First_quantization
Elementary particles with a spin of 1/2
Spin-1/2 objects are all fermions (a fact explained by the spin–statistics theorem) and satisfy the Pauli exclusion principle. Spin-1/2 particles can have
Spin_1/2
Method of quantum computing
{\displaystyle K_{i}} generators of the stabilizer group. The Gottesman–Knill theorem states that, given a set of logic gates from the Clifford group, followed
One-way_quantum_computer
Predecessor to modern quantum mechanics (1900–1925)
= k T {\displaystyle 1/\beta =kT} . This reproduces the equipartition theorem of classical thermodynamics: every harmonic oscillator at temperature T
Old_quantum_theory
Quantum mechanical state change
Olival (2006-12-01). "Philosophy enters the optics laboratory: Bell's theorem and its first experimental tests (1965–1982)". Studies in History and Philosophy
Spontaneous_emission
Principle in quantum information science
Quantum simulation Qubit physical vs. logical Quantum processors cloud-based Theorems Bell's Eastin–Knill Gleason's Gottesman–Knill Holevo's No-broadcasting
Monogamy_of_entanglement
Quantum-mechanical version of computer memory
quantum computing, this is forbidden because, according to the no clone theorem, any quantum state cannot be reproduced completely. Therefore, in the absence
Quantum_memory
Formulations of quantum mechanics
expectation values yields the Ehrenfest theorem featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger
Dynamical_pictures
Apparent lack of definite state before measurement of quantum systems
Hermitian) operator A on H. If H is finite dimensional, by the spectral theorem, A has an orthonormal basis of eigenvectors. If the system is in state
Quantum_indeterminacy
Special low-energy state in quantum mechanics
strong advocate of Einstein's locality-first perspective, proved Bell's theorem and showed that it could be used to assess the existence or non-existence
Singlet_state
Theory to explain the emergence of the classical world from the quantum world
Kastner, Ruth E. (2014). "'Einselection' of pointer observables: The new H-theorem?". Studies in History and Philosophy of Science Part B: Studies in History
Quantum_Darwinism
Physics experiment in quantum mechanics
states of the idler photons at their four distinct detection screens. A theorem proven by Phillippe Eberhard shows that if the accepted equations of relativistic
Delayed-choice_quantum_eraser
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ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
ELITZURS THEOREM
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