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npj Quantum Information

The entropic cost of quantum generalized measurements

Luca Mancino, Marco Sbroscia, Emanuele Roccia, Ilaria Gianani, Fabrizia Somma, Paolo Mataloni, Mauro Paternostro, Marco Barbieri

Published Mar 7, 2018• 20 citations
Publisher

Abstract

Abstract Landauer’s principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors.

DOI
10.1038/s41534-018-0069-z

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Abstract Landauer’s principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors.
Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our new entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach can provide on building blocks of quantum information processors.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
Information and energy are intrinsically linked. The more information an experimenter holds about the state of a physical system, the more effectively it can be used to extract useful energy. Conversely, to force the system from an unknown state into a known state costs energy. Landauer’s principle cements this connection: in erasing a bit of information, at least kT ln 2 of energy must be dissipated. Now, with the advent of quantum technologies and as features of integrated circuits approach atomic scales, it is a good time to re-examine the relationship between energy and information in quantum contexts. This thesis covers three main themes. The first examines the energy cost of quantum information operations. Unlike many previous treatments, our approach recognises that it is not sufficient to transform the average density matrix of input signals to the average output, but instead each individual signal must be mapped correctly. By constructing optimal protocols, we quantify a uniquely quantum extra cost arising from this more constrained problem. The second part explores the energy cost of erasing classical information encoded in quantum dots, with reference to two experiments. In the first, work done on the dot is measured via back-action on the vibrations of a carbon nanotube. In agreement with a parallel theoretical investigation, the results indicate that lifetime broadening, a quantum strong coupling effect, dominates the exchange rate between work and information in the device. We also outline the design of an experiment into the effect of potential difference on erasure cost. Finally, we consider the role of particle exchange symmetry. We introduce a scheme in which symmetry is encoded into a latent degree of freedom, such that the statistics can interpolate between Bose-Einstein and Fermi-Dirac. We study the thermal properties of such a system, including ways in which a fermion-boson phase transition could aid the performance of thermodynamic cycles.
The Landauer's principle, a cornerstone of information thermodynamics, provides a fundamental lower bound on the energetic cost of information erasure in terms of the information content change. However, its traditional formulation is largely confined to systems exchanging solely energy with an ideal thermal bath. In this work, we derive general information-cost trade-off relations that go beyond the scope of Landauer's principle by developing a thermodynamic inference approach based on the maximum entropy principle. These relations require only information about the system and are applicable to complex quantum scenarios involving multiple conserved charges and non-thermal environments. Specifically, we present two key results: (i) In scenarios where only the mean values of observables are accessible, we derive an information-content-informed upper bound on the thermodynamic cost which complements an existing generalized Landauer lower bound. (ii) When second-order fluctuations can also be measured, we obtain an information-content-informed lower bound on the change in variances of observables, thereby extending the Landauer's principle to constrain higher-order fluctuation costs. We numerically validate our information-cost trade-off relations using a coupled-qubit system exchanging energy and excitations, a driven qubit implementing an information erasure process, and a driven double quantum dot system that can operate as an inelastic heat engine. Our results underscore the broad utility of maximum-entropy inference in constraining thermodynamic costs for generic finite-time quantum processes, with direct relevance to quantum information processing and quantum thermodynamic applications.