On the Conservation of Information in Quantum Physics

Antoine Browaeys

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In this article, we discuss through a principle of action the quantum information in relation to the information paradox.The information paradox, which arises in black hole physics, suggests that information can be lost when matter falls into a black hole, which contradicts the principle of information conservation in physics.We propose that the principle of action, which asserts that the action of a physical system is conserved, can be applied to information, showing that information is conserved in a similar way to energy and momentum.Through mathematical models and theoretical analysis, we show that the conservation of information can be understood as a result of the evolution of a system and probability amplitudes in quantum mechanics.

Chris Timpson

Jianming Cai, Xiang-Fa Zhou, Zheng-Wei Zhou +1 more

We use fidelity to characterize the information about a quantum state contained in another quantum state. In a multi-qubit system, each qubit has individual information about a prescribed quantum state. We investigate how the total information changes under the interactions of nonlocal Hamiltonians. We show that for some special physical interactions the total information is conserved. This type of nonlocal Hamiltonians are named as Conservative Hamiltonians, similar to the Conservative Forces. We then apply this Information Conservation Law in the quantum spin system, and propose methods for improving the efficiency of quantum communications through an open end spin chain.

Michał Horodecki, Ryszard Horodecki, Aditi Sen De +1 more

We show that the no-deleting and no-cloning principles are implications of information conservation principle. This is unlike in classical physics, where cloning and deleting are possible, independently of information conservation. Connections with the second law of thermodynamics are also discusssed.

Gregg S. Jaeger