Entropic uncertainty relations - A survey

Abstract

Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, rather little is known about entropic uncertainty relations with more than two measurement settings. In this note we review known results and open questions.

12 pages, revtex

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Cited by in corpus (260)

• Advances in Quantum Cryptography
• On mutually unbiased bases
• Entropic Uncertainty Relations and their Applications
• Quantum Steering
• The uncertainty principle determines the non-locality of quantum mechanics
• Quantum Cryptography Beyond Quantum Key Distribution
• Quantum discord and its allies: a review
• Improved entropic uncertainty relations and information exclusion relations
• Uncertainty relations from simple entropic properties
• The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction
• Universal Uncertainty Relations
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Majorization entropic uncertainty relations
• Strong Majorization Entropic Uncertainty Relations
• How well can one jointly measure two incompatible observables on a given quantum state?
• Tightening the entropic uncertainty bound in the presence of quantum memory
• Entropic uncertainty relations for multiple measurements
• A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography
• Equivalence of wave-particle duality to entropic uncertainty
• Mutually unbiased measurements in finite dimensions
• Characterization of high-dimensional entangled systems via mutually unbiased measurements
• Quantum-memory-assisted entropic uncertainty principle under noise
• Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies
• Entanglement sampling and applications
• Quantum-memory-assisted entropic uncertainty relations
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Self-testing mutually unbiased bases in the prepare-and-measure scenario
• Information theoretic treatment of tripartite systems and quantum channels
• Steering criteria from general entropic uncertainty relations
• Device-Independent Quantum Key Distribution with Random Key Basis
• Majorization Formulation of Uncertainty in Quantum Mechanics
• Variance-based uncertainty relations
• Optimized entropic uncertainty relations for multiple measurements
• Correlation complementarity yields Bell monogamy relations
• An equality between entanglement and uncertainty
• Quantum and classical entropic uncertainty relations
• Operational framework for quantum measurement simulability
• General entropy-like uncertainty relations in finite dimensions
• Entanglement detection using mutually unbiased measurements
• Experimental test of Heisenberg's measurement uncertainty relation based on statistical distances
• A min-entropy uncertainty relation for finite size cryptography
• Collision entropy and optimal uncertainty
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
• Entropic uncertainty from effective anti-commutators
• Notes on general SIC-POVMs
• A violation of the uncertainty principle implies a violation of the second law of thermodynamics
• Information complementarity: A new paradigm for decoding quantum incompatibility
• A family of generalized quantum entropies: definition and properties
• The Link between Entropic Uncertainty and Nonlocality
• Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
• Lower bound of quantum uncertainty from extractable classical information
• Generalized Pauli channels and a class of non-Markovian quantum evolution
• On uncertainty relations and entanglement detection with mutually unbiased measurements
• Weighted Uncertainty Relations
• The Smooth Entropy Formalism for von Neumann Algebras
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Sum uncertainty relations based on Wigner-Yanase skew information
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Position-momentum uncertainty relations based on moments of arbitrary order
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Relations for certain symmetric norms and anti-norms before and after partial trace
• Variance-based uncertainty relations for incompatible observables
• Controlling entropic uncertainty bound through memory effects
• Complementary sequential measurements generate entanglement
• Multi-observable Uncertainty Relations in Product Form of Variances
• Entropic uncertainty relations for extremal unravelings of super-operators
• Entanglement witnesses from mutually unbiased bases
• Implications and applications of the variance-based uncertainty equalities
• Measurement uncertainty relations for discrete observables: Relative entropy formulation
• Uncertainty relations for quantum coherence with respect to mutually unbiased bases
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Optimized entropic uncertainty relation for successive measurement
• Quantum Complementarity through Entropic Certainty Principles
• Entropic uncertainty relations in multidimensional position and momentum spaces
• Extended quantum conditional entropy and quantum uncertainty inequalities
• Entropic uncertainty relations from quantum designs
• On the connection between Complementarity and Uncertainty Principles in the Mach-Zehnder interferometric setting
• Compatible quantum correlations: on extension problems for Werner and isotropic states
• Stronger steerability criterion for more uncertain continuous variable systems
• Variance uncertainty relations without covariances for three and four observables
• Contradictory uncertainty relations
• Entanglement Detection Using Majorization Uncertainty Bounds
• The Conditional Uncertainty Principle
• Separability criteria via sets of mutually unbiased measurements
• State-independent preparation uncertainty relations
• Quantum to Classical Randomness Extractors
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Uncertainty, joint uncertainty, and the quantum uncertainty principle
• Constructing Mutually Unbiased Bases from Quantum Latin Squares
• Majorization entropic uncertainty relations for quantum operations
• Experimental Schmidt Decomposition and Entanglement Detection
• Quantum-memory-assisted entropic uncertainty relation with a single nitrogen-vacancy center in diamond
• Maximum nonlocality and minimum uncertainty using magic states
• Entropic formulation of the uncertainty principle for the number and annihilation operators
• Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
• Entropic trade-off relations for quantum operations
• Uncertainty relations from graph theory
• On a generalized entropic uncertainty relation in the case of the qubit
• Device-independent tests of quantum measurements
• Majorization uncertainty relations for mixed quantum states
• Certainty relations, mutual entanglement and non-displacable manifolds
• Uncertainty Relations for coarse-grained measurements: an overview
• Improved quantum entropic uncertainty relations
• Fine-grained uncertainty relation and biased non-local games in bipartite and tripartite systems
• Information-theoretic equilibrium and observable thermalization
• Controlling the entropic uncertainty lower bound in two-qubit systems under the decoherence
• Conjectured strong complementary-correlations tradeoff
• Maximally informative ensembles for SIC-POVMs in dimension 3
• Alternative measures of uncertainty in quantum metrology: Contradictions and limits
• Uncertainty and certainty relations for complementary qubit observables in terms of Tsallis' entropies
• Entropic uncertainty relations with quantum memory in a multipartite scenario
• Tight Bounds on the Accessible Information and the Informational Power
• Fine-grained uncertainty relations for several quantum measurements
• Realization of mutually unbiased bases for a qubit with only one wave plate: Theory and experiment
• Fine-grained uncertainty relation and nonlocality of tripartite systems
• Asymptotic entropic uncertainty relations
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Optimal uncertainty relations in a modified Heisenberg algebra
• Exact Energy-Time Uncertainty Relation for Arrival Time by Absorption
• Spin-orbit-coupled quantum memory of a double quantum dot
• Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures
• A transform of complementary aspects with applications to entropic uncertainty relations
• Multipartite correlations in mutually unbiased bases
• Uncertainties of genuinely incompatible triple measurements based on statistical distance
• Steering is an essential feature of non-locality in quantum theory
• Comparative analysis of information measures of the Dirichlet and Neumann two-dimensional quantum dots
• Unruh effect without trans-horizon entanglement
• Accessible Information and Informational Power of Quantum 2-designs
• Detecting non-Markovianity via uncertainty relations
• Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
• Entropic measures of joint uncertainty: effects of lack of majorization
• A geometric formulation of uncertainty principle
• On entropic uncertainty relations in the presence of a minimal length
• Measurement uncertainty relations for position and momentum: Relative entropy formulation
• Separability conditions based on local fine-grained uncertainty relations
• Quantum uncertainty relation based on the mean deviation
• Achieving the physical limits of the bounded-storage model
• Entropic Uncertainty Relations and the Quantum-to-Classical transition
• Geometric uncertainty relation for mixed quantum states
• Building one-time memories from isolated qubits
• Entropic uncertainty relations and the stabilizer formalism
• Joint measurability, steering and entropic uncertainty
• Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Bell monogamy relations in arbitrary qubit networks
• Quantum Measurements in the Light of Quantum State Estimation
• Optimal potentials for diffusive search strategies
• Tripartite measurement uncertainty in Schwarzschild space-time
• Capacities of Gaussian Quantum Channels with Passive Environment Assistance
• Hierarchy of Bounds on Accessible Information and Informational Power
• The minimal length and the Shannon entropic uncertainty relation
• The general fine-grained uncertainty relation and the second law of thermodynamics
• Quantum information measures of the one-dimensional Robin quantum well
• Estimating the Shannon entropy and (un)certainty relations for design-structured POVMs
• Conditional entropic uncertainty relations for Tsallis entropies
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• Multipartite entanglement detection based on generalized state-dependent entropic uncertainty relation for multiple measurements
• Quantum-information theory of magnetic field influence on circular dots with different boundary conditions
• Higher-order statistical correlations and mutual information among particles in a quantum well
• Entropic uncertainty relations for SIC-POVMs and MUMs
• Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order $\alpha \in (0;1]$
• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Unified-entropy trade-off relations for a single quantum channel
• A finite geometric toy model of space-time as an error correcting code
• Optimized state independent entanglement detection based on geometrical threshold criterion
• Renyi entropy of the totally asymmetric exclusion process
• Entropic uncertainty relations for successive generalized measurements
• Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells
• Single-shot security for one-time memories in the isolated qubits model
• Fine-grained uncertainty relation under the relativistic motion
• Measures of disturbance and incompatibility for quantum measurements
• Photonic quantum data locking
• A disturbance tradeoff principle for quantum measurements
• Unveiling quantum steering by quantum-classical uncertainty complementarity
• An entropic analysis of approximate quantum error correction
• Entropic uncertainty relations for multiple measurements assigned with biased weights
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory
• Mutually unbiased bases with free parameters
• Uncertainty relations for quantum measurements from generalized equiangular tight frames
• On entropic uncertainty relations for measurements of energy and its "complement"
• Towards Quantum One-Time Memories from Stateless Hardware
• Near-Optimal Variance-Based Uncertainty Relations
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Measurement uncertainty from no-signaling and non-locality
• Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• An improved bound for strong unitary uncertainty relations with refined sequence
• Optimal Universal Uncertainty Relations
• Uncertainty and certainty relations for successive projective measurements of a qubit in terms of Tsallis' entropies
• Entropic uncertainty relation for pointer-based simultaneous measurements of conjugate observables
• Improved unitary uncertainty relations
• Summation and product forms of uncertainty relations based on metric-adjusted skew information
• New inequalities for quantum von Neumann and tomographic mutual information
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Entropic distinguishability of quantum fields in phase space
• Role of complementarity in superdense coding
• Weak locking capacity of quantum channels can be much larger than private capacity
• The Operational Choi-Jamiolkowski Isomorphism
• New Examples of Kochen-Specker Type Configurations on Three Qubits
• Deriving the Qubit from Entropy Principles
• Quantum conditional entropies and steerability of states with maximally mixed marginals
• Rényi Entropy, Signed Probabilities, and the Qubit
• Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
• Operational measure of incompatibility of noncommuting observables
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Separability and entanglement of spin $1$ particle
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• Notes on entropic characteristics of quantum channels
• Average of uncertainty-product for bounded observables
• Uncertainty relations based on state-dependent norm of commutator
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario
• Metric and classical fidelity uncertainty relations for random unitary matrices
• Enhanced Information Exclusion Relations
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Uncertainty relations for the support of quantum states
• On optimal cloning and incompatibility
• The role of interparticle interaction and environmental coupling in a two-particle open quantum system
• Complementary properties of multiphoton quantum states in linear optics networks
• Geometric uncertainty relation for quantum ensembles
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Entropic Bounds For Unitary Testers and Mutually Unbiased Unitary Bases
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels
• Quantum Uncertainty Equalities and Inequalities for Unitary Operators
• Optimizing incompatible triple quantum measurements
• Rényi and Tsallis formulations of separability conditions in finite dimensions
• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$
• Entropic Bounds as Uncertainty Measure of Unitary Operators
• Distribution of Standard deviation of an observable among superposed states
• Individual attacks with generalized discrimination and inadequacy of some information measures
• Flavor-mass majorization uncertainty relations and their links to the mixing matrix
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits
• Uncertainty Relations and Indistinguishable Particles
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• The effects of different quantum feedback types on the tightness of the variance-based uncertainty
• On fully entangled fraction and quantum conditional entropies for states with maximally mixed marginals
• Uniform Entanglement Frames
• Entanglement detection with scrambled data
• Inequalities for the quantum privacy
• A combined-probability space and (un)certainty relations for a finite-level quantum system
• Spin minimum uncertainty states for refined uncertainty relations
• Limitations imposed by complementarity
• Deformed entropic and information inequalities for X - states of two-qubit and single qudit states
• Entropic uncertainty under indefinite causal order and input-output direction
• Entropic measurement uncertainty relations for all the infinite components of a spin vector
• Uncertainty principle certifies genuine source of intrinsic randomness
• Mutually equibiased bases
• Classical noise and the structure of minimal uncertainty states
• Universal quantum uncertainty relations: minimum-uncertainty wave packet depends on measure of spread
• Observing tight triple uncertainty relations in two-qubit systems
• Uncertainty, von Neumann Entropy, and Squeezing in a Bipartite State of Two-Level Atoms
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
• Quantum Separability Criteria Based on Symmetric Measurements
• Quantum Uncertainty and Entropy
• Confidence uncertainty: position and momentum can be jointly determined with a guaranteed probability
• Information and majorization theory for fermionic phase-space distributions