Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Philosophy of Science

Quantum Randomness and Underdetermination

Jeffrey Alan Barrett, Simon M. Huttegger

Published Feb 20, 2020• 22 citations
Publisher

Abstract

We consider the nature of quantum randomness and how one might have empirical evidence for it. We will see why, depending on one’s computational resources, it may be impossible to determine whether a particular notion of randomness properly characterizes one’s empirical data. Indeed, we will see why even an ideal observer under ideal epistemic conditions may never have any empirical evidence whatsoever for believing that the results of one’s quantum-mechanical experiments are randomly determined. This illustrates a radical sort of empirical underdetermination faced by fundamentally stochastic theories like quantum mechanics.

DOI
10.1086/708712

Related papers

Empirical Ontology and Explanation

Jeffrey Alan Barrett

Abstract Each formulation of quantum mechanics we consider in the book seeks to explain why we have determinate measurement records distributed according to the standard quantum statistics. The explanation we get relies on the metaphysical assumptions that underlie the particular theory. Metaphysics here does real explanatory work in accounting for our experience. While it is not at all clear what specific metaphysical commitments best explain our experience, one can distinguish between different types and degrees of empirical adequacy each formulation provides. Stronger notions of empirical adequacy might be characterized in terms of such things as the plausibility that one’s experience in fact supervenes on the sort of records a particular theory provides and the richness of the account of experience provided by the theory.

•Dec 26, 2019•0 citations

Is “Physical Randomness” Just Indeterminism in Disguise?

Paul W. Humphreys

The topic of this session is “physical randomness”. It might be doubted whether such a subject exists, for definitions of randomness have hitherto almost all been mathematical in nature. The only exceptions of which I am aware are the preceding paper by Benioff and a paper by Wesley Salmon. These attempts to inject some empirical content into randomness are highly desirable. But anyone attempting to formulate a physically based definition of randomness should at some point make clear what the connection is (if any) with a more traditional notion of disorder - that of indeterminism. Repeated reference to quantum mechanical examples whenever physical randomness is discussed indicates that a primary motivation for considering physical randomness to be important is because of the current belief that data sequences associated with quantum mechanical experiments are irreducibly random. (As an indication of this, in any situation in which physical randomness is discussed, translate the remarks about quantum phenomena into remarks about coin tossing, and they will lose much of their interest.)

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1978•6 citations

Quantum Information with Meaning Inside and Outside the Quantum

Alastair A. Abbott, Cristian S. Calude, Karl Svozil

The ability to transfer information securely is essential in the modern world we live in. While the field of cryptography has long researched ways to do this, events over the last couple of years have brought the issues of secure information transfer squarely into the public eye. As a consequence, security and cryptography have quickly become issues of social and political importance, sparking debates about the values of privacy and the role of government. An essential ingredient of modern cryptography is the generation of randomness: cryptographic techniques are built on the premise that one has access to random bits. It is well known, however, that computers cannot produce algorithmically random sequences – that is, sequences with maximal algorithmic information content – but are doomed to produce ‘pseudorandomness’. This lack of randomness can be, and has been, exploited to compromise security, see [4]. The active field of quantum information theory has proposed approaches to provide supposedly ‘unbreakable’ security by exploiting various quantum phenomena. This security unfortunately relies on assumptions about the nature of quantum measurements and their ability to generate random bits. Anton Zeilinger summarises this by postulating that the simplest quantum systems, qubit, can hold only one bit of classical information [6]. This foundational principle is in line with a wider paradigm shift to view quantum information as an extension of classical information, but it is nonetheless unsatisfying to simply postulate this principle, given its importance in determining the practical advantages of quantum information theory. In order to understand better how quantum mechanics can help generate meaningful information, we instead look to relate the outcomes of quantum measurements to formal properties of the system based on more fundamental assumptions. Indeed, we have shown that a) some of the postulated properties of quantum information follow from the formal structure of the theory and b) a purely formal notion of information within a quantum world can generate, via measurement, meaningful and useful information in the macroscopic world (for example, in cryptography). The indeterminism of quantum measurements can be formalised via the notion of value indefiniteness. To explain this concept, let us consider an arbitrary quantum system and ask whether the outcome of a measurement of any observable quantity A (such as the energy of the system, its angular momentum (spin), etc.) is determined prior to the measurement. If this is the case, then we say the observable is value definite with value v(A); otherwise, the observable is value indefinite and v(A) is undefined. Mathematically, one can reduce all observable quantities to so-called projection observables, which can only take the values 0 or 1. Thus, the question of whether the outcome of several measurements can be simultaneously determined in advance can be rephrased in terms of the information ‘carried’ by a particular system in a definite quantum state. Classically, one expects that all quantities are determined in advance, and hence all observables are value definite. Quantum mechanically, however, the belief is that this is not the case, and the information content of quantum systems is limited. Formulating carefully the notion of value indefiniteness allows us to formalise the notion of (quantum) indeterminism; however, this doesn’t help clarify whether quantum systems are indeed value indefinite or not. Staying in this formal framework, the Kochen-Specker theorem [5] provides a first positive result, showing that at least some observables must be value indefinite if one makes the assumption known as non-contextuality, which states that any definite values that exist must be independent of other compatible measurements that may or may not be performed on the system. Under the same assumption, this theorem can be strengthened to show that only one single observable can have the definite value 1 (see [2]). Furthermore, only observables that can be measured simultaneously with this single one can have the definite value 0; the rest must all be value indefinite. Since the preparation of a system involves precisely ensuring that, usually via measurement, the system is in a definite state with respect to some desired observable, this result shows that no other incompatible observable can be value definite. That is, preparing a system in a definite state by making the ‘preparation’ observable value definite specifies completely the information content of the quantum system. This is an example of syntactical quantum information acquiring meaning at the level of the quantum itself. Can the syntactical information at the level of the quantum generate meaning outside the quantum, that is, at the macroscopic level? The results cited above hold in the Hilbert-space framework of quantum mechanics and are formulated only in terms of a syntactical notion of information. Their real importance becomes evident when one interprets them in the context of quantum measurements. Specifically, if we prepare a quantum system in a known state, they allow us to ‘locate’ observables which we can measure, but which are value indefinite; that is, observables whose measurement results are not specified by any pre-existing property of the quantum system. Furthermore, with respect to a mathematical model of unpredictability which we developed in [3], the results of these measurements can be shown to be absolutely unpredictable. In this way we get a mathematical explanation and justification of the largely accepted intuition that quantum mechanics is inherently unpredictable, and that this unpredictability arises from the phenomenon of indefiniteness within the quantum world. Furthermore, if one considers a hypothetical infinite sequence generated by the repeated measurement of a quantum value indefinite observable, one can prove that these sequences must be strongly incomputable, technically ‘bi-immune’ [1]. Such sequences cannot be generated by any Turing machine or classical computer, showing that value indefiniteness leads to a clear classical/quantum split in a purely algorithmic context. Importantly, bi-immunity is a property of observed, macroscopic quantities, quite separate from the quantum framework in which the value indefiniteness is formalised. This form of macroscopic meaning created from the lack of syntactic information is precisely the scenario that quantum random number generators try to create, and which is essential for the development and certification of quantum cryptographic systems. The fact that the macroscopic information created goes beyond anything classically obtainable serves as a valuable practical resource, outside of and removed from the quantum formalism. To conclude, quantum information creates meaning within the quantum and via measure- ment, the lack of information within the quantum, creates meaning and valuable information at the macroscopic level. Acknowledgments The second author thanks Prof. S. Marcus for useful conversations on quantum information theory. This work was supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant RANPHYS. References and Notes Abbott, A.A.; Calude, C.S.; Svozil, K. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A 2012, 86, 062109. Abbott, A.A.; Calude, C.S.; Svozil, K. Value-indefinite observables are almost everywhere. Physical Review A 2013, 89, 032109. Abbott, A.A.; Calude, C.S.; Svozil, K. On the unpredictability of individual quantum measurement outcomes. CDMTCS Research Report 2014, 458. Calude, C.S. Quantum randomness & cryptology. CyberTalk 2013, 3, 42–43. Kochen, S.; Specker, E. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 1967, 17, 59–87. Zeilinger, A. A foundational principle for quantum mechanics. Foundations of Physics 1999, 29(4),631–643.

ISIS Summit: The Information Society at the Crossroads•Jun 23, 2015•0 citations

Quantum Phenomena

Jeffrey Alan Barrett

Abstract The behavior of electrons provides several concrete examples of quantum phenomena. We consider electron spin properties, how electrons move, quantum randomness and the relationships between observables, quantum limits on empirical prediction, superpositions, interference effects, nonlocality, and the role of observation in generating quantum phenomena. Each illustrates the counterintuitive nature of quantum phenomena and provides a sense of the sort of phenomena that any satisfactory formulation of quantum mechanics must predict and explain.

•Dec 26, 2019•0 citations

RANDOMNESS AND CAUSALITY IN QUANTUM PHYSICS Eleven famous quantum experiments

Pier Sandro Scano

Quantum Physics is usually defined as a theory that affirms a primary role of randomness and probability. Eleven well-known quantum experiments are examined and the result is the coexistence of both random and causal type behaviour. We need both to describe experiments. Quantum Mechanics states the general overcoming of causality and this statement constitutes an unlimited generalization, not supported by experience. Determinism and indeterminism are philosophical systems, that universalize causality or chance. The crucial point is the difference between epistemic and intrinsic randomness. In the first aspect, randomness does not have a fundamental meaning, in the second, randomness of the individual event is explained, but the detection of high stable regularities remains to be explained. The article addresses the question of entanglement and various aspects of probability theory, including the law of large numbers, arriving at the thesis that many relevant questions are unresolved. A causal description is in quantum mechanics impossible in principle, given its assumptions. In order not to contradict experience, both points of view are necessary, causal and random. This is the state of the research, to return to and start again from.

•Oct 16, 2024•0 citations

The quantum world and the completeness of quantum mechanics

James T. Cushing

What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]

Cambridge University Press eBooks•Jan 29, 1998•0 citations
We consider the nature of quantum randomness and how one might have empirical evidence for it. We will see why, depending on one’s computational resources, it may be impossible to determine whether a particular notion of randomness properly characterizes one’s empirical data. Indeed, we will see why even an ideal observer under ideal epistemic conditions may never have any empirical evidence whatsoever for believing that the results of one’s quantum-mechanical experiments are randomly determined. This illustrates a radical sort of empirical underdetermination faced by fundamentally stochastic theories like quantum mechanics.
Abstract Each formulation of quantum mechanics we consider in the book seeks to explain why we have determinate measurement records distributed according to the standard quantum statistics. The explanation we get relies on the metaphysical assumptions that underlie the particular theory. Metaphysics here does real explanatory work in accounting for our experience. While it is not at all clear what specific metaphysical commitments best explain our experience, one can distinguish between different types and degrees of empirical adequacy each formulation provides. Stronger notions of empirical adequacy might be characterized in terms of such things as the plausibility that one’s experience in fact supervenes on the sort of records a particular theory provides and the richness of the account of experience provided by the theory.
The topic of this session is “physical randomness”. It might be doubted whether such a subject exists, for definitions of randomness have hitherto almost all been mathematical in nature. The only exceptions of which I am aware are the preceding paper by Benioff and a paper by Wesley Salmon. These attempts to inject some empirical content into randomness are highly desirable. But anyone attempting to formulate a physically based definition of randomness should at some point make clear what the connection is (if any) with a more traditional notion of disorder - that of indeterminism. Repeated reference to quantum mechanical examples whenever physical randomness is discussed indicates that a primary motivation for considering physical randomness to be important is because of the current belief that data sequences associated with quantum mechanical experiments are irreducibly random. (As an indication of this, in any situation in which physical randomness is discussed, translate the remarks about quantum phenomena into remarks about coin tossing, and they will lose much of their interest.)
The ability to transfer information securely is essential in the modern world we live in. While the field of cryptography has long researched ways to do this, events over the last couple of years have brought the issues of secure information transfer squarely into the public eye. As a consequence, security and cryptography have quickly become issues of social and political importance, sparking debates about the values of privacy and the role of government. An essential ingredient of modern cryptography is the generation of randomness: cryptographic techniques are built on the premise that one has access to random bits. It is well known, however, that computers cannot produce algorithmically random sequences – that is, sequences with maximal algorithmic information content – but are doomed to produce ‘pseudorandomness’. This lack of randomness can be, and has been, exploited to compromise security, see [4]. The active field of quantum information theory has proposed approaches to provide supposedly ‘unbreakable’ security by exploiting various quantum phenomena. This security unfortunately relies on assumptions about the nature of quantum measurements and their ability to generate random bits. Anton Zeilinger summarises this by postulating that the simplest quantum systems, qubit, can hold only one bit of classical information [6]. This foundational principle is in line with a wider paradigm shift to view quantum information as an extension of classical information, but it is nonetheless unsatisfying to simply postulate this principle, given its importance in determining the practical advantages of quantum information theory. In order to understand better how quantum mechanics can help generate meaningful information, we instead look to relate the outcomes of quantum measurements to formal properties of the system based on more fundamental assumptions. Indeed, we have shown that a) some of the postulated properties of quantum information follow from the formal structure of the theory and b) a purely formal notion of information within a quantum world can generate, via measurement, meaningful and useful information in the macroscopic world (for example, in cryptography). The indeterminism of quantum measurements can be formalised via the notion of value indefiniteness. To explain this concept, let us consider an arbitrary quantum system and ask whether the outcome of a measurement of any observable quantity A (such as the energy of the system, its angular momentum (spin), etc.) is determined prior to the measurement. If this is the case, then we say the observable is value definite with value v(A); otherwise, the observable is value indefinite and v(A) is undefined. Mathematically, one can reduce all observable quantities to so-called projection observables, which can only take the values 0 or 1. Thus, the question of whether the outcome of several measurements can be simultaneously determined in advance can be rephrased in terms of the information ‘carried’ by a particular system in a definite quantum state. Classically, one expects that all quantities are determined in advance, and hence all observables are value definite. Quantum mechanically, however, the belief is that this is not the case, and the information content of quantum systems is limited. Formulating carefully the notion of value indefiniteness allows us to formalise the notion of (quantum) indeterminism; however, this doesn’t help clarify whether quantum systems are indeed value indefinite or not. Staying in this formal framework, the Kochen-Specker theorem [5] provides a first positive result, showing that at least some observables must be value indefinite if one makes the assumption known as non-contextuality, which states that any definite values that exist must be independent of other compatible measurements that may or may not be performed on the system. Under the same assumption, this theorem can be strengthened to show that only one single observable can have the definite value 1 (see [2]). Furthermore, only observables that can be measured simultaneously with this single one can have the definite value 0; the rest must all be value indefinite. Since the preparation of a system involves precisely ensuring that, usually via measurement, the system is in a definite state with respect to some desired observable, this result shows that no other incompatible observable can be value definite. That is, preparing a system in a definite state by making the ‘preparation’ observable value definite specifies completely the information content of the quantum system. This is an example of syntactical quantum information acquiring meaning at the level of the quantum itself. Can the syntactical information at the level of the quantum generate meaning outside the quantum, that is, at the macroscopic level? The results cited above hold in the Hilbert-space framework of quantum mechanics and are formulated only in terms of a syntactical notion of information. Their real importance becomes evident when one interprets them in the context of quantum measurements. Specifically, if we prepare a quantum system in a known state, they allow us to ‘locate’ observables which we can measure, but which are value indefinite; that is, observables whose measurement results are not specified by any pre-existing property of the quantum system. Furthermore, with respect to a mathematical model of unpredictability which we developed in [3], the results of these measurements can be shown to be absolutely unpredictable. In this way we get a mathematical explanation and justification of the largely accepted intuition that quantum mechanics is inherently unpredictable, and that this unpredictability arises from the phenomenon of indefiniteness within the quantum world. Furthermore, if one considers a hypothetical infinite sequence generated by the repeated measurement of a quantum value indefinite observable, one can prove that these sequences must be strongly incomputable, technically ‘bi-immune’ [1]. Such sequences cannot be generated by any Turing machine or classical computer, showing that value indefiniteness leads to a clear classical/quantum split in a purely algorithmic context. Importantly, bi-immunity is a property of observed, macroscopic quantities, quite separate from the quantum framework in which the value indefiniteness is formalised. This form of macroscopic meaning created from the lack of syntactic information is precisely the scenario that quantum random number generators try to create, and which is essential for the development and certification of quantum cryptographic systems. The fact that the macroscopic information created goes beyond anything classically obtainable serves as a valuable practical resource, outside of and removed from the quantum formalism. To conclude, quantum information creates meaning within the quantum and via measure- ment, the lack of information within the quantum, creates meaning and valuable information at the macroscopic level. Acknowledgments The second author thanks Prof. S. Marcus for useful conversations on quantum information theory. This work was supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant RANPHYS. References and Notes Abbott, A.A.; Calude, C.S.; Svozil, K. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A 2012, 86, 062109. Abbott, A.A.; Calude, C.S.; Svozil, K. Value-indefinite observables are almost everywhere. Physical Review A 2013, 89, 032109. Abbott, A.A.; Calude, C.S.; Svozil, K. On the unpredictability of individual quantum measurement outcomes. CDMTCS Research Report 2014, 458. Calude, C.S. Quantum randomness & cryptology. CyberTalk 2013, 3, 42–43. Kochen, S.; Specker, E. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 1967, 17, 59–87. Zeilinger, A. A foundational principle for quantum mechanics. Foundations of Physics 1999, 29(4),631–643.
Abstract The behavior of electrons provides several concrete examples of quantum phenomena. We consider electron spin properties, how electrons move, quantum randomness and the relationships between observables, quantum limits on empirical prediction, superpositions, interference effects, nonlocality, and the role of observation in generating quantum phenomena. Each illustrates the counterintuitive nature of quantum phenomena and provides a sense of the sort of phenomena that any satisfactory formulation of quantum mechanics must predict and explain.
Quantum Physics is usually defined as a theory that affirms a primary role of randomness and probability. Eleven well-known quantum experiments are examined and the result is the coexistence of both random and causal type behaviour. We need both to describe experiments. Quantum Mechanics states the general overcoming of causality and this statement constitutes an unlimited generalization, not supported by experience. Determinism and indeterminism are philosophical systems, that universalize causality or chance. The crucial point is the difference between epistemic and intrinsic randomness. In the first aspect, randomness does not have a fundamental meaning, in the second, randomness of the individual event is explained, but the detection of high stable regularities remains to be explained. The article addresses the question of entanglement and various aspects of probability theory, including the law of large numbers, arriving at the thesis that many relevant questions are unresolved. A causal description is in quantum mechanics impossible in principle, given its assumptions. In order not to contradict experience, both points of view are necessary, causal and random. This is the state of the research, to return to and start again from.
What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]