Conceptual Inadequacy of the Shannon Information in Quantum Measurements
arXiv:quant-ph/0006087 · doi:10.1103/PhysRevA.63.022113
Abstract
In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior to and independent of observation. Because of the completely different root of a quantum measurement as compared to a classical measurement conceptual difficulties arise when we try to define the information gain in a quantum measurement using the notion of Shannon information. The reason is that, in contrast to classical measurement, quantum measurement, with very few exceptions, cannot be claimed to reveal a property of the individual quantum system existing before the measurement is performed.
11 pages, 5 figures, important Ref. [6] is now cited in all appropriate places
References in corpus (2)
Cited by in corpus (62)
- Quantum Mechanics as Quantum Information (and only a little more)
- Operationally Invariant Information in Quantum Measurements
- Formulation of the uncertainty relations in terms of the Renyi entropies
- Mutually unbiased binary observable sets on N qubits
- Distinct Quantum States Can Be Compatible with a Single State of Reality
- Entropic Uncertainty Relations in Quantum Physics
- Quantum theory from questions
- Determining a quantum state by means of a single apparatus
- Exact uncertainty relations: physical significance
- Information Invariance and Quantum Probabilities
- Influence of the interaction range on the thermostatistics of a classical many-body system
- Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements
- An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism
- Frobenius-norm-based measures of quantum coherence and asymmetry
- Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits
- Young's experiment and the finiteness of information
- Toolbox for reconstructing quantum theory from rules on information acquisition
- Spreading lengths of Hermite polynomials
- Nonadditive measure and quantum entanglement in a class of mixed states of N^n-system
- Differential entropy and time
- On Interferometric Duality in Multibeam Experiments
- Quantum-Bayesian Coherence
- Quantum theory from rules on information acquisition
- Contradictory uncertainty relations
- Types of quantum information
- Foundations of quantum theory and quantum information applications
- Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables
- Consistency of the Shannon entropy in quantum experiments
- A toy model for quantum mechanics
- Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
- Channel kets, entangled states, and the location of quantum information
- A nonextensive critical phenomenon scenario for quantum entanglement
- Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
- Alternative measures of uncertainty in quantum metrology: Contradictions and limits
- Quantum Non-Objectivity from Performativity of Quantum Phenomena
- On the Brukner-Zeilinger approach to information in quantum measurements
- Logical Entropy for Quantum States
- Frontier between separability and quantum entanglement in a many spin system
- Angular performance measure for tighter uncertainty relations
- Total variance and invariant information in complementary measurements
- The Significance of Information in Quantum Theory
- Quantum logical entropy: fundamentals and general properties
- Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications
- Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation
- Information-Probabilistic description of the Universe
- Real or Not Real that is the question
- On conclusive eavesdropping and measures of mutual information in quantum key distribution
- Certainty relations between local and nonlocal observables
- Towards an information description of space-time
- Complexity of the XY antiferromagnet at fixed magnetization
- Probing the Information-Probabilistic Description
- General framework of quantum complementarity from a measurement-based perspective
- Critique du rapport signal à bruit en théorie de l'information -- A critical appraisal of the signal to noise ratio in information theory
- Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets
- Information entropy and nucleon correlations in nuclei
- Relating measurement disturbance, information and orthogonality
- Individual attacks with generalized discrimination and inadequacy of some information measures
- Information and Errors in Quantum Teleportation
- Enabling the Network to Surf the Internet
- Uncertainty conservation relations: theory and experiment
- On non-commutativity in quantum theory (I): from classical to quantum probability
- The Grammar of Teleportation