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Physical Review Letters

Experimental Verification of Dissipation-Time Uncertainty Relation

L.-L. Yan, Jiawei Zhang, M.-R. Yun, J.-C. Li, G.-Y. Ding, J.-F. Wei, J.-T. Bu, B. Wang, Liang Chen, Shi‐Lei Su, Fei Zhou, Ya Jia, Erjun Liang, Mang Feng

Published Feb 4, 2022• 32 citations
Publisher

Abstract

Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.

DOI
10.1103/physrevlett.128.050603

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Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.
The quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics.Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production.Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state.Furthermore, we carry out experimental verification of this informationtheoretical bound by means of a single spin embedded in an ultracold trapped 40 Ca + ion.Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.
We derive an operationally defined lower bound on the physical time Δt \Delta t Δtrequired to execute any information-processing task, based on the total entropy produced ΔΣ \Delta\Sigma ΔΣ. The central result, Δt≥τΣΔΣ \Delta t \geq \tau_{\Sigma} \Delta\Sigma Δt≥τΣ​ΔΣ, introduces the Process-Dependent Dissipation Timescale τΣ≡1/⟨Σ˙⟩max \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} τΣ​≡1/⟨Σ˙⟩max​, which quantifies the maximum achievable entropy production rate for a given physical platform. We derive τΣ \tau_{\Sigma} τΣ​ from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:Δtmeas≥τΣkB[H(P)−S(ρ)] \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] Δtmeas​≥τΣ​kB​[H(P)−S(ρ)], relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.
Quantum thermodynamic uncertainty relations establish fundamental trade-offs between the precision achievable in quantum systems and associated thermodynamic quantities such as entropy production or dynamical activity. While foundational, empirical demonstrations have thus far been confined to specific cases, either assuming time-reversal symmetry or involving particular measurement types, leaving the verification of their universal validity unrealized. This work leverages a quantum computer to present the first empirical verification of a general quantum thermodynamic uncertainty relation, valid for arbitrary dynamics and observables. We theoretically derive the relation, identifying survival activity as the pivotal thermodynamic quantity governing the precision bound. The verification is demonstrated on IBM's cloud-based quantum processor, which is treated as a real thermodynamic system. To achieve accurate results despite substantial device errors, we introduce a generic protocol for measuring survival activity and employ circuit reduction techniques based on the relation's properties. This strategy allows us to empirically measure survival activity for the first time and confirm the derived relation. Furthermore, the quantum computer's versatility enables the implementation of optimal observables, leading to the saturation of the relation and demonstrating the sharpness of our bound on a physical device. The method's broad applicability is further illustrated by verifying the trade-off for quantum time correlators. Our findings establish quantum computers as effective platforms for investigating fundamental thermodynamic trade-off relations.
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.
Thermodynamic uncertainty relations (TURs) are a set of inequalities expressing a fundamental trade-off between precision and dissipation in nonequilibrium classical and quantum thermodynamic processes. TURs show that achieving low fluctuations in a thermodynamic quantity (e.g., heat or work) requires a minimum entropy production, with profound implications for the efficiency of biological and artificial thermodynamic processes. The accurate evaluation of TURs is a necessary requirement to quantify the fluctuation and dissipation entailed by a thermodynamic process, and ultimately to optimize the performance of quantum devices, whose operation is fundamentally a quantum thermodynamic process. Here, we simulate TURs in a transverse-field Ising model subjected to a time-dependent driving protocol, using quantum and classical computers in concert. Varying the duration and strength of the drive as well as the system size, we verify the validity of TURs, identify quantum signatures in the work statistics within the linear response regime, and observe TUR saturation in the high-temperature limit.
We derive a fundamental uncertainty principle relating entropy change and time: for any quantum system coupled to a thermal environment, the entropy change ΔS and the characteristic timescale Δt satisfy ΔS·Δt ≥ kᴪ/2. We call this the Parker Relation. The derivation proceeds from the quantum Thermodynamic Uncertainty Relation (quantum TUR) of Hasegawa and Van Vu [Phys. Rev. E 99, 062126 (2019)], which holds for all quantum channels without restriction to quasi-static or equilibrium processes. We provide a second independent derivation from the canonical commutation relations of the entropy field operator Ś = ∫Φ√(-g) d³x, which yields the same bound through the Robertson inequality. Four immediate consequences are derived with explicit numerical predictions: (1) a minimum information erasure time of 18.4 femtoseconds at 300 K, establishing a fundamental floor on computational switching speed beyond any engineering constraint; (2) a minimum decoherence time of 53 nanoseconds for a 5 GHz superconducting transmon qubit at 20 mK; (3) an exponential suppression of high-frequency vacuum modes that removes 119 orders of magnitude from the cosmological constant ultraviolet divergence; and (4) a characteristic thermodynamic timescale of ~15 ms for living cells at physiological metabolic rates, coinciding with observed neural and cellular signaling timescales. The Parker Relation is interpretation-independent: it holds in Copenhagen, many-worlds, and objective collapse frameworks equally. It is the temporal complement of Landauer’s principle and the thermodynamic analog of the Heisenberg energy-time uncertainty relation.