Philippe Faist

The minimum amount of thermodynamic work required in order to implement a quantum computation or a quantum state transformation can be quantified using frameworks based on the resource theory of thermodynamics, deeply rooted in the works of Landauer and Bennett. For instance, the work we need to invest in order to implement n independent and identically distributed (i.i.d.) copies of a quantum channel is quantified by the thermodynamic capacity of the channel when we require the implementation's accuracy to be guaranteed in diamond norm over the n-system input. Recent work showed that work extraction can be implemented universally, meaning the same implementation works for a large class of input states, while achieving a variable work cost that is optimal for each individual i.i.d. input state. Here, we revisit some techniques leading to derivation of the thermodynamic capacity, and leverage them to construct a thermodynamic implementation of n i.i.d. copies of any time-covariant quantum channel, up to some process decoherence that is necessary because the implementation reveals the amount of consumed work. The protocol uses so-called thermal operations and achieves the optimal per-input work cost for any i.i.d. input state; it relies on the conditional erasure protocol in our earlier work, adjusted to yield variable work. We discuss the effect of the work-cost decoherence. While it can significantly corrupt the correlations between the output state and any reference system, we show that for any time-covariant i.i.d. input state, the state on the output system faithfully reproduces that of the desired process to be implemented. As an immediate consequence of our results, we recover recent results for optimal work extraction from i.i.d. states up to the error scaling and implementation specifics, and propose an optimal preparation protocol for time-covariant i.i.d. states.

Abstract Noise in quantum metrology reduces the sensitivity to which one can determine an unknown parameter in the evolution of a quantum state, such as time. Here, we consider a probe system prepared in a pure state that evolves according to a given Hamiltonian. We study the resulting local sensitivity of the probe to time after the application of a given noise channel. We show that the decrease in sensitivity due to the noise is equal to the sensitivity that the environment gains with respect to the energy of the probe. We obtain necessary and sufficient conditions for when the probe does not suffer any sensitivity loss; these conditions are analogous to, but weaker than, the Knill-Laflamme quantum error correction conditions. New upper bounds on the sensitivity of the noisy probe are obtained via our uncertainty relation, by applying known sensitivity lower bounds on the environments system. Our time-energy uncertainty relation also generalizes to any two arbitrary parameters whose evolutions are generated by Hermitian operators. This uncertainty relation asserts a general trade-off between the sensitivities that two parties can achieve for any two respective parameters of a single quantum system, in terms of the commutator of the associated generators. We consider applications to strongly interacting many-body probes. We find probe states for general interaction graphs of Ising and Heisenberg interactions that are robust to any single located error. For a 1D spin chain with nearest-neighbor interactions subject to amplitude damping noise on each site, we verify numerically that our probe state does not lose any sensitivity to first order in the noise parameter.

We study quantum information transmission through noisy multi-time processes, modeled as quantum combs that capture temporal correlations across multiple time steps. We focus on communication tasks in which admissible recovery operations are used to simulate an identity channel in the presence of environmental action over multiple time steps. Within this framework, we define the capacity of a quantum comb as the maximal number of qubits that can be transmitted with a given error. We provideSDP-computable converse bounds on both the maximal rate and error exponent for arbitrary combs. In particular, we introduce multi-time non-signaling and positive partial transpose (PPT) codes and develop a multi-time analogue of the Rains bound. As an application, we analyze the simulation of a temporally correlated depolarizing channel. We also obtain multi-time analogues of hypothesis-testing quantities under restricted multi-time measurements and their associated entropic quantities, which we believe to be of independent interest.

A many-body system, whether in contact with a large environment or evolving under complex dynamics, can typically be modeled as occupying the thermal state singled out by Jaynes' maximum entropy principle. Here, we find analogous fundamental principles identifying a noisy quantum channel $\mathcal{T}$ to model the system's dynamics, going beyond the study of its final equilibrium state. Our maximum channel entropy principle states that $\mathcal{T}$ should maximize the channel's entropy, suitably defined, subject to any available macroscopic constraints. These may correlate input and outputs, and may lead to restricted or partial thermalizing dynamics such as thermalization with average energy conservation. This principle is reinforced by an independent extension of the microcanonical derivation of the thermal state to channels, which leads to the same $\mathcal{T}$. Our technical contributions include a derivation of the general mathematical structure of $\mathcal{T}$, a custom postselection theorem relating an arbitrary permutation-invariant channel to nearby i.i.d. channels, as well as novel typicality results for quantum channels for noncommuting constraints and arbitrary input states. We propose a learning algorithm for quantum channels based on the maximum channel entropy principle, demonstrating the broader relevance of $\mathcal{T}$ beyond thermodynamics and complex many-body systems.