Conservation of information and the foundations of quantum mechanics (original) (raw)
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Information and the Reconstruction of Quantum Physics
Annalen der Physik
The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra-mathematical content. Here, a representative series of specifically information-based treatments-from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems-is reviewed.
Informational derivation of quantum theory
We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.
Quantum Theory is an Information Theory
Foundations of Physics, 2015
We derive quantum theory from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of information processing that can be regarded as standard. One postulate-purification-singles out quantum theory within this class.
Quantum-Informational Principles for Physics
The Frontiers Collection, 2015
It is time to to take a pause of reflection on the general foundations of physics, reexamining the solidity of the most basic principles, as the relativity and the equivalence principles that are currently under dispute for violations at the Planck scale. A constructive criticism engages us in seeking new general principles, which reduce to the old ones as approximations holding in the physical domain already explored. At the very basis of physics are epistemological and operational rules for the same formulability of the physical law and for the computability of its theoretical predictions, rules that give rise to new solid principles. These rules lead us to a quantum-information theoretic formulation, hinging on a logical identification of the experimental protocol with the quantum algorithm.
Informational axioms for quantum theory
2012
It was recently proved that quantum theory can be derived from six axioms about information processing. Here we review these axioms, discussing various facets of their information-theoretical nature, and illustrating the general picture of quantum physics that emerges from them.
A Foundational Principle for Quantum Mechanics
Synthese Library
In contrast to the theories of relativity, quantum mechanics is not yet based on a generally accepted conceptual foundation. It is proposed here that the missing principle may be identified through the observation that all knowledge in physics has to be expressed in propositions and that therefore the most elementary system represents the truth value of one proposition, i.e., it carries just one bit of information. Therefore an elementary system can only give a definite result in one specific measurement. The irreducible randomness in other measurements is then a necessary consequence. For composite systems entanglement results if all possible information is exhausted in specifying joint properties of the constituents.
This essay consists of two main parts: In the first (Sec.1-2), I consider the challenges that an information theoretic reconstruction of quantum mechanics (QM) faces if it aspires to provide fundamental explanatory power. In the second (Sec.3), I sketch a scenario in which most of these challenges are met, as a proof of concept. In the first part, I argue that the main challenge for reconstructions with the above aspiration is to provide a constructive model in the sense of Einstein. In the second part, I argue that upon the assumption that QM is a theory developed by (a certain notion of) observers, there can be constructive models of QM involving classical information. Sec.4 finishes with a summary and conclusion.
Entanglement as an axiomatic foundation for statistical mechanics
arXiv:1608.04459 [quant-ph], 2016
We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms---Causality, Purity Preservation, Pure Sharpness, and Purification---identify a class of theories where every mixed state can be modelled as the marginal of a pure entangled state and where every unsharp measurement can be modelled as a sharp measurement on a composite system. This class of theories, called sharp theories with purification, includes quantum theory both with complex and real amplitudes, as well as a suitable extension of classical probability theory where classical systems can be entangled with other, non-classical systems. Theories satisfying our axioms support well-behaved notions of majorization, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. We conjecture that every theory admitting a sensible thermodynamics must be extendable to a sharp theory with purification.
Information and the Quantum World
Entropy, 2016
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.
Principle of information causality rationalizes quantum composition
Cornell University - arXiv, 2022
Anchoring the abstract mathematical formulation of Hilbert space quantum mechanics on physical ground is one of the long standing pursuits of quantum foundational research. Here we show that the principle of information causality, a generalization of no signaling principle, plays significant role to this aim. In accordance with no-signaling condition, state and effect spaces of a composite system can allow different possible mathematical descriptions even when the individual systems are assumed to be quantum. While in one extreme the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, in the other extreme it contains only separable states and the resulting theory becomes local. As we show, none of these compositions does commensurate with information causality, and hence get invalidated to be the bona-fide description of nature. Information causality, therefore, promises physical ground towards self-duality of state and effect cones for composite quantum systems.