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Scientific Reports

Irreversible and quantum thermodynamic considerations on the quantum zeno effect

Umberto Lucia

Published Jul 4, 2023• 3 citations
Publisher

Abstract

The quantum zeno effect slows down the quantum system's time evolution under frequent measurements. This paper aims to study this quantum effect by introducing the definition of time based on an irreversible thermodynamic analysis of quantum systems. Consequently, the quantum zeno effect requires (i) high values of the electromagnetic entropy generation rate related to the spontaneously down-converted light and (ii) a decrease in the quantum system's entropy value. So, the quantum zeno effect is a quantum process related to the interaction between a quantum system and the electromagnetic waves of the measurement device, causing a quantum thermodynamic stationary state. Last, the fundamental role of irreversibility emerges.

DOI
10.1038/s41598-023-38040-w

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The quantum zeno effect slows down the quantum system's time evolution under frequent measurements. This paper aims to study this quantum effect by introducing the definition of time based on an irreversible thermodynamic analysis of quantum systems. Consequently, the quantum zeno effect requires (i) high values of the electromagnetic entropy generation rate related to the spontaneously down-converted light and (ii) a decrease in the quantum system's entropy value. So, the quantum zeno effect is a quantum process related to the interaction between a quantum system and the electromagnetic waves of the measurement device, causing a quantum thermodynamic stationary state. Last, the fundamental role of irreversibility emerges.
If a measurement process is regarded as an irreversible process, then by Second law of thermodynamics the entropy should increase after any measurement process. By the same spirit a quantum system undergoing repeated measurement should show strong irreversibility leading to entropy production. On the contrary we show that in quantum Zeno effect setting the entropy of a quantum system decreases and goes to zero after a large number of measurements. We discuss the entropy change under continuous measurement model and show that entropy can decrease if we use a more accurate measuring apparatus.
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.
If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula, we will give a characterization of the quantum Zeno effect for finite-rank projections in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its (not necessarily bounded from below) generator as a generalized mean value Hamiltonian.
The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.
A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ``collapse of the wave function'' is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann's projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.
According to the quantum Zeno effect (QZ), frequent observations of a system can dramatically slow down its dynamical evolution. We show that the QZ is a physical consequence of the statistical indistinguishability of neighboring quantum states. The time scale of the problem is expressed in terms of the Fisher information and we demonstrate that the Zeno dynamics of particle entangled states might require quite smaller measurement intervals than classically correlated states. We propose an interferometric experiment to test the prediction.