Non-commutative effects in physical processes

It is argued that in order to address the mind/matter relationship, we will have to radically change the conceptual structure normally assumed in physics. Rather than fields and/or particles-in-interaction described in the traditional Cartesian order based a local evolution in spacetime, we need to introduce a more general notion of process described by a non-commutative algebra. This will have radical implications for both for physical processes and for geometry. By showing how the Bohm interpretation of quantum mechanics can be understood within a non-commutative structure, we can give a much clearer meaning to the implicate order introduced by Bohm. It is through this implicate order that mind and matter can be seen as different aspects of the same general process.It is argued that in order to address the mind/matter relationship, we will have to radically change the conceptual structure normally assumed in physics. Rather than fields and/or particles-in-interaction described in the traditional Cartesian order based a local evolution in spacetime, we need to introduce a more general notion of process described by a non-commutative algebra. This will have radical implications for both for physical processes and for geometry. By showing how the Bohm interpretation of quantum mechanics can be understood within a non-commutative structure, we can give a much clearer meaning to the implicate order introduced by Bohm. It is through this implicate order that mind and matter can be seen as different aspects of the same general process.

AIP conference proceedingsJan 1, 200145 citations

Irreversible Processes in Physical Theory

R. C. L. Bosworth

NatureFeb 8, 195811 citations

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Nina H. Amini, Zibo Miao, Yu Pan +2 more

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.

arXiv:1406.4599EPJ Quantum TechnologyJun 16, 20157 citations

Quantum Mechanical Processes

Pure and applied physicsJan 1, 19700 citations

Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology

Ningxin Kong, Haojie Wang, Mingsheng Tian +4 more

A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$ , which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$ . Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$ , exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$, exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.

quant-pharXiv:2511.22280Physical Review LettersNov 28, 20253 citations

Noncommutative Dynamics

Jakub Rembieliński

Springer eBooksJan 1, 19931 citation

\mathcal{K}

, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite

\mathcal{K}

yields an enhanced scaling of root-mean-square error as

N^{-(1+\mathcal{K})}

. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit

\mathcal{K} \to \infty

, exponential precision scaling

N^{-1}e^{-N}

is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.