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

arXiv:1401.1012 · Journal of the Korean Physical Society

Consistent theory for causal non-locality beyond the Born’s rule

Wonmin Son

Published Feb 1, 2014• 5 citations
arXivHTMLPDF

Abstract

According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of a non-local box . The concept has been introduced from the principle of non-locality, which satisfies relativistic causality. In this paper, we show that a correlation leading to the non-local box can be derived consistently if we release one of major axioms in quantum mechanics, Born’s rule . This allows us to obtain a theory that in one end of the spectrum agrees with the classical probability and in the other end agrees with the theory of non-local causality. At the same time, we argue that the correlation lies in a space with special mathematical constraints such that a physical realization of the correlation through a probability measure is not possible in one direction of its limit, but is possible in the other limit.

DOI
10.3938/jkps.64.499

Related papers

Quantum probability assignment limited by relativistic causality

Yeong Deok Han, Taeseung Choi

Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.

Scientific Reports•Mar 14, 2016•5 citations

A measurable physical theory of hyper-correlations beyond quantum mechanics

Tristan Farrow, Vlatko Vedral, Wonmin Son

Abstract A unique characteristic of quantum mechanics is entanglement describing correlations between particles irrespective of their locations. This property, called non-locality, has no classical analogue. Over the past few years, quantum physicists have reached a consensus that we lack a physical theory to account for a class of states whose non-local character exceeds the bounds allowed by quantum mechanics. Motivated by our observation that an extension of the Schrödinger equation with non-linear terms is directly linked to a relaxation of Born’s rule, an axiom of quantum mechanics, we derive a physical theory that accounts for such hyper-correlated states and modifies Born’s rule. We model correlated particles with a generalized probability theory whose dynamics are described with a non-linear version of Schrödinger’s equation and demonstrate how that deviates from the standard formulation of quantum mechanics in experimental probability-prediction. We show also that the violation of the Clauser-Horn-Shimony-Holt inequality, the amount of non-locality, is proportional to the degree of non-linearity, which can be experimentally tested.

Physica Scripta•Oct 29, 2020•0 citations

Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule

Jérémie Harris, Frédéric Bouchard, Enrico Santamato +3 more

The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. A major family of derivations is based on envariance, a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Further, we demonstrate envariance in a purely local quantum system, showing its independence from relativistic causality.

arXiv:1604.01471•New Journal of Physics•May 11, 2016•13 citations

Stronger-than-quantum bipartite correlations violate relativistic causality in the classical limit

Daniel Rohrlich

Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound from the axioms of nonlocality, relativistic causality and the existence of a classical limit. This derivation of Tsirelson's bound does not assume quantum mechanics yet suggests how Hilbert space is implicit in quantum correlations.

arXiv:1408.3125•Aug 13, 2014•4 citations

Causality and Non-Locality in Quantum Mechanics: An argument for retrocausation

Jørn Kløvfjell Mjelva

It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.

•Jan 1, 2017•0 citations

No causal order and quantum probability assignment

Yeong Deok Han, Taeseung Choi

We have studied how relativistic causality limits on the generalization of quantum probability assignment, which can give more nonlocal (superquantum) correlations than quantum correlations. We have shown that 'no causal order' condition between two spacelike separate events is stronger than no faster-than-light-signaling condition as the requirement of relativistic causality. Using no causal order condition we have proved that Born rule is the only probability assignment to quantum measurement on an arbitrary entangled quantum state described by the Hilbert space language, consistent with relativistic causality. We have also shown that all superquantum correlations, which preserve relativistic causality, can be understood as hypothetical correlations given by applying modified quantum probability assignments to quantum measurements on a Bell state.

arXiv:1307.2026•Jul 8, 2013•0 citations
According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of a non-local box . The concept has been introduced from the principle of non-locality, which satisfies relativistic causality. In this paper, we show that a correlation leading to the non-local box can be derived consistently if we release one of major axioms in quantum mechanics, Born’s rule . This allows us to obtain a theory that in one end of the spectrum agrees with the classical probability and in the other end agrees with the theory of non-local causality. At the same time, we argue that the correlation lies in a space with special mathematical constraints such that a physical realization of the correlation through a probability measure is not possible in one direction of its limit, but is possible in the other limit.
Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.
Abstract A unique characteristic of quantum mechanics is entanglement describing correlations between particles irrespective of their locations. This property, called non-locality, has no classical analogue. Over the past few years, quantum physicists have reached a consensus that we lack a physical theory to account for a class of states whose non-local character exceeds the bounds allowed by quantum mechanics. Motivated by our observation that an extension of the Schrödinger equation with non-linear terms is directly linked to a relaxation of Born’s rule, an axiom of quantum mechanics, we derive a physical theory that accounts for such hyper-correlated states and modifies Born’s rule. We model correlated particles with a generalized probability theory whose dynamics are described with a non-linear version of Schrödinger’s equation and demonstrate how that deviates from the standard formulation of quantum mechanics in experimental probability-prediction. We show also that the violation of the Clauser-Horn-Shimony-Holt inequality, the amount of non-locality, is proportional to the degree of non-linearity, which can be experimentally tested.
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. A major family of derivations is based on envariance, a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Further, we demonstrate envariance in a purely local quantum system, showing its independence from relativistic causality.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.
We have studied how relativistic causality limits on the generalization of quantum probability assignment, which can give more nonlocal (superquantum) correlations than quantum correlations. We have shown that 'no causal order' condition between two spacelike separate events is stronger than no faster-than-light-signaling condition as the requirement of relativistic causality. Using no causal order condition we have proved that Born rule is the only probability assignment to quantum measurement on an arbitrary entangled quantum state described by the Hilbert space language, consistent with relativistic causality. We have also shown that all superquantum correlations, which preserve relativistic causality, can be understood as hypothetical correlations given by applying modified quantum probability assignments to quantum measurements on a Bell state.