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Constraints on energy distribution in spacetime
Quantum inequalities are local constraints on the magnitude and extent of distributions of negative energy density in space-time. Initially conceived to
Quantum_inequalities
Theorem in physics
have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments
Bell's_theorem
Physics phenomenon
with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science". Just as energy is a resource that facilitates
Quantum_entanglement
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 cannot
CHSH_inequality
Concept in Hlibert spaces mathematics
many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with
Trace_inequality
Hypothetical FTL transportation by warping space
mass–energy, when described in the context of the quantum field theories. If certain quantum inequalities conjectured by Ford and Roman hold, the energy
Alcubierre_drive
Deviations from local realism
correlations of measurement results. If the Bell inequalities are violated experimentally as predicted by quantum mechanics, then reality cannot be described
Quantum_nonlocality
Experiments to test Bell's theorem in quantum mechanics
Bell inequality violations are also used in some quantum cryptography protocols, whereby a spy's presence is detected when Bell's inequalities cease
Bell_test
Foundational principle in quantum physics
mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such
Uncertainty_principle
Hypothetical topological feature of spacetime
quantum inequality". Gravity and Cosmology. 46 (2006): 195. arXiv:gr-qc/0409007. Bibcode:2006GrCo...12..195K. Krasnikov, Serguei (2003). "The quantum
Wormhole
Apparent lack of definite state before measurement of quantum systems
In diametrical contrast, in the case of quantum physics, the theorems of Kochen and Specker, the inequalities of John Bell, and experimental evidence
Quantum_indeterminacy
Experimentally violated inequality of correlations of entangled particles
rather than the Leggett inequalities. Given that experimental tests of Bell's inequalities have ruled out local realism in quantum mechanics, the violation
Leggett_inequality
Concept in quantum entanglement
Quantum pseudo-telepathy describes the use of quantum entanglement to eliminate the need for classical communications. A nonlocal game is said to display
Quantum_pseudo-telepathy
Relationship of various quantum subsystems
references here include: "Quantum Computation and Quantum Information" "Quantum Entropy and Its Use" Trace Inequalities and Quantum Entropy: An Introductory
Strong subadditivity of quantum entropy
Strong_subadditivity_of_quantum_entropy
Term in quantum mechanics
In quantum mechanics, notably in quantum information theory, fidelity quantifies the "closeness" between two density matrices. It expresses the probability
Fidelity_of_quantum_states
Area of physical and philosophical debate
interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Quantum mechanics
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Concept in physics
Hongwei Yu and Weixing Shu; "Quantum states with negative energy density in the Dirac field and quantum inequalities", Physics Letters B, Volume 570
Negative_energy
Rules in probabilistic logic
In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George Boole and explicitly
Fréchet_inequalities
Mathematical inequality representing macroscopic objects
inequalities in Bell test experiments, which plays an important role in understanding the nature of the Einstein–Podolsky–Rosen paradox. Here quantum
Leggett–Garg_inequality
Force resulting from the quantisation of a field
L. H.; Roman, Thomas A. (1995). "Averaged Energy Conditions and Quantum Inequalities". Physical Review D. 51 (8): 4277–4286. arXiv:gr-qc/9410043. Bibcode:1995PhRvD
Casimir_effect
Interdisciplinary theory behind quantum computing
"Bell's Inequalities: Foundations and Quantum Communication". arXiv:0909.2611 [quant-ph]. Braunstein, S. L. (2005). "Entanglement in Quantum Information
Quantum_information_science
Description of physical properties at the atomic and subatomic scale
disciplines, including quantum chemistry, quantum biology, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe
Quantum_mechanics
Historical critique of quantum mechanics
unable to reproduce the quantum mechanical correlations. This difference, expressed using inequalities known as "Bell inequalities", is in principle experimentally
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Interaction of a quantum system with a classical observer
violates the statistical conditions known as Bell inequalities indicates that the unpredictability of quantum measurement results cannot be explained away
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Non-mathematical introduction
suggested, physicists have found that nature obeys quantum mechanics and violates Bell inequalities. In other words, the results of these experiments are
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
French physicist (born 1947)
with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science". In 2025 he was elected to the Académie
Alain_Aspect
Mathematics of general relativity
vacuum energy is positive for a conducting sphere.) However, various quantum inequalities suggest that a suitable averaged energy condition may be satisfied
Energy_condition
Mathematical inequality relating inner products and norms
"A survey on Cauchy–Bunyakovsky–Schwarz type discrete inequalities", Journal of Inequalities in Pure and Applied Mathematics, 4 (3): 142 pp, archived
Cauchy–Schwarz_inequality
Theoretical upper limit to non-local correlations in quantum mechanics
an upper limit to quantum mechanical correlations between distant events. Given that quantum mechanics violates Bell inequalities (i.e., it cannot be
Tsirelson's_bound
Context dependence in quantum measurements
noncontextuality inequalities (also known as generalized Bell inequalities). With respect to certain appropriately normalised inequalities, the independence
Quantum_contextuality
American mathematical physicist
works pertain to the quantum and classical many-body problems, atomic structure, the stability of matter, functional inequalities, the theory of magnetism
Elliott_H._Lieb
Quantum mechanics experiment
Aspect's experiment was the first quantum mechanics experiment to demonstrate the violation of Bell's inequalities with photons using distant detectors
Aspect's_experiment
Continuous (non-quantized) quantities in quantum information science
function approximation, high-dimensional integration and quantum cryptography. Quantum inequalities Weedbrook, Christian; Pirandola, Stefano; García-Patrón
Continuous-variable quantum information
Continuous-variable_quantum_information
Loss of quantum coherence
Quantum decoherence is the loss of quantum coherence. It involves generally a loss of information of a system to its environment. Quantum decoherence
Quantum_decoherence
Description of gravity using discrete values
Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals
Quantum_gravity
Interpretation of quantum mechanics
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wave function is objectively real, and
Many-worlds_interpretation
Quantum mechanical phenomenon
In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or
Quantum_tunnelling
Northern Irish physicist (1928–1990)
continuing to believe that Bell's inequalities must fail. Bell remained interested in objective "observer-free" quantum mechanics. He felt that at the most
John_Stewart_Bell
Mathematical entity to describe the probability of each possible measurement on a system
In quantum physics, a quantum state is a mathematical entity that represents a physical system. Quantum mechanics specifies the construction, evolution
Quantum_state
Inequality in mathematical physics
are named after E. H. Lieb and W. E. Thirring. The inequalities are useful in studies of quantum mechanics and differential equations and imply, as a
Lieb–Thirring_inequality
Principle of quantum mechanics
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are
Quantum_superposition
Fact that observing a situation changes it
effect occurs in quantum mechanics, as demonstrated by the double-slit experiment. Physicists have found that observation of quantum phenomena by a detector
Observer_effect_(physics)
Class of inequalities
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f {\displaystyle f} , its logarithm, and
Logarithmic Sobolev inequalities
Logarithmic_Sobolev_inequalities
Quantum mechanical model
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually
Quantum_harmonic_oscillator
Swedish theoretical physicist
mathematical physics and quantum information theory, having to do with open quantum systems, entropy inequalities, and quantum measurements. Lindblad was
Göran_Lindblad_(physicist)
Type of entropy in quantum theory
quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics, and it is the quantum counterpart
Von_Neumann_entropy
Apparent unusual observation in the sky
pioneering NACA/NASA aerospace engineer. Krasnikov, S. (2003). "The quantum inequalities do not forbid spacetime shortcuts". Physical Review D. 67 (10) 104013
Unidentified_flying_object
Quantum states of two qubits
quantum information science, the Bell's states or EPR pairs are specific quantum states of two qubits that represent the simplest examples of quantum
Bell_state
Cryptography based on quantum mechanical phenomena
called BB84, the first Quantum Key Distribution system. Independently, in 1991 Artur Ekert proposed to use Bell's inequalities to achieve secure key distribution
Quantum_cryptography
Aspect of quantum measurement
distribution ρ(λ). The quantum correlation is the key statistic in the CHSH inequality and some of the other Bell inequalities, tests that open the way
Quantum_correlation
Notation for conserved quantities in physics and chemistry
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the
Quantum_number
Secure communication method
Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol based on the laws of quantum mechanics, specifically
Quantum_key_distribution
Physical phenomenon
Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation
Quantum_teleportation
Networks connecting quantum processors
Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information
Quantum_network
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
Sub-field of quantum physics and optics
establishing the violation of Bell inequalities and pioneering quantum information science". According to quantum theory, light may be considered not
Quantum_optics
Physics experiment in quantum mechanics
A delayed-choice quantum eraser experiment is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's
Delayed-choice_quantum_eraser
Type of quantum mechanics theory
probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables. The mathematical formulation of quantum mechanics assumes
Hidden-variable_theory
Austrian quantum physicist (born 1945)
with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. Anton Zeilinger was born in 1945 in
Anton_Zeilinger
American physicist (born 1942)
with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science". In 2023, he declared himself as a climate
John_Clauser
Theoretical problem in quantum physics
In quantum mechanics, the measurement problem is the problem of definite outcomes: quantum systems have superpositions but quantum measurements only give
Measurement_problem
American mathematician (born 1931)
established these inequalities for the Bosonic and Fermionic cases. The inequalities were named by Gross, who established the inequalities in dimension-independent
Leonard_Gross
Physical principle that only immediate surroundings can influence an object
quantum mechanics broadly violates Bell's inequalities. According to some interpretations of quantum mechanics, this result implies that some quantum
Principle_of_locality
Quantum mechanics thought experiment
dramatic illustration of non-classicality than other quantum phenomena like the violation of Bell inequalities. The argument from Spekkens toy model involves
Elitzur–Vaidman_bomb_tester
Austrian theoretical physicist (born 1945)
standard textbook Anomalies in Quantum Field Theory, and in the field of Bell inequalities, in particular from the quantum comparison Bertlmann’s Socks
Reinhold_Bertlmann
Theorem of convex functions
} This inequality naturally extends to C*-algebras equipped with a finite trace and is particularly useful in applications ranging from quantum statistical
Jensen's_inequality
timeline of quantum computing and communication. Erwin Schrödinger publishes a theorem setting the basis for quantum steering and the limits of quantum state
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Physics textbook
Absorption, emission and scattering of photons by atoms Quantum entanglement, measurements, Bell's inequalities Appendices Bernd Crasemann writing for the American
Quantum_Mechanics_(book)
Encoding an n-bit string in m qubits
Quantum random access codes (QRACs) are a quantum information theoretic primitive used to encode a string of classical bits into a quantum state of smaller
Quantum_random_access_code
Dutch physicist (born 1969)
Terhal, “Bell Inequalities and The Separability Criterion”, Physics Letters A 271, 319 (2000) B.M. Terhal and D.P. DiVincenzo, “Adaptive quantum computation
Barbara_Terhal
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Interpretation of quantum mechanics
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being relational, that is,
Relational_quantum_mechanics
In quantum chemistry and physics, the Lieb–Oxford inequality provides a lower bound for the indirect part of the Coulomb energy of a quantum mechanical
Lieb–Oxford_inequality
Interdisciplinary research area
Quantum machine learning (QML) is the study of quantum algorithms for machine learning. It often refers to quantum algorithms for machine learning tasks
Quantum_machine_learning
Theory of logic to account for observations from quantum theory
analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The formal
Quantum_logic
Any entity that can be measured
the set of all possible system states, e.g., position and momentum. In quantum mechanics, an observable is described by a linear operator. For example
Observable
Truths and principles of the study of matter, space, time and energy
have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments
Philosophy_of_physics
Different states of quantum systems
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels
Energy_level
Quantum
inequalities are tight. That is, there is a decomposition for which the second inequality is saturated, which is the same as stating that the quantum
Quantum_Fisher_information
Elementary particle or quantum of light
φῶς, φωτός (phôs, phōtós) 'light') is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such
Photon
Interpretation of quantum mechanics
Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max
Copenhagen_interpretation
Problem in statistical physics
December 2015). "Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities". Studies in Mathematical
Stability_of_matter
Application of quantum theory mathematics to cognitive phenomena
Quantum cognition uses the mathematical formalism of quantum probability theory to model psychology phenomena when classical probability theory fails.
Quantum_cognition
Physics experiment
In quantum mechanics, a quantum eraser experiment is an interferometer experiment that demonstrates several fundamental aspects of quantum mechanics,
Quantum_eraser_experiment
Requirement that quantum states' time evolution operators are unitary transformations
In quantum physics, unitarity (process) is the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically
Unitarity
Relativistic quantum mechanical wave equation
of quantum mechanics and the theory of special relativity, and was the first theory to fully account for special relativity in the context of quantum mechanics
Dirac_equation
Quantum mechanics principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e., fermions) cannot simultaneously
Pauli_exclusion_principle
Process by which a quantum system takes on a definitive state
In various interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially
Wave_function_collapse
Calculation rule in quantum mechanics
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly
Born_rule
Interpretation of quantum mechanics
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These
Local_hidden-variable_theory
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question
Quantum_chaos
Theorem in functional analysis
arXiv:2606.00247 [math.FA]. Boris Tsirelson (1987). "Quantum analogues of the Bell inequalities. The case of two spatially separated domains" (PDF). Journal
Grothendieck_inequality
Correlation inequality in statistical mechanics
Fröhlich, J.; Park, Y.M. (1978). "Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems". Comm. Math. Phys. 59
Griffiths_inequality
Physics experiment
way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]." If one illuminates two parallel
Double-slit_experiment
Cloud quantum computing platform
IBM Quantum Platform (previously known as IBM Quantum Experience) is an online platform allowing public and premium access to cloud-based quantum computing
IBM_Quantum_Platform
Remote quantum processors for computation
Cloud-based quantum computing refers to the remote access of quantum computing resources—such as quantum emulators, simulators, or processors—via the internet
Cloud-based_quantum_computing
Predecessor to modern quantum mechanics (1900–1925)
The old quantum theory is a collection of results from the years 1900–1925, which predate modern quantum mechanics. The theory was never complete or self-consistent
Old_quantum_theory
Concept in information theory
Inequalities are very important in the study of information theory. There are a number of different contexts in which these inequalities appear. Consider
Inequalities in information theory
Inequalities_in_information_theory
Diagram used to represent quantum field theory calculations
used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise
Spin_network
Special low-energy state in quantum mechanics
In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term "singlet" originally meant a linked set of
Singlet_state
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