Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features. Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states. In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relationfollowing a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system. Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.The verification and use of quantum fluctuation relations [1][2][3] requires the design of experimentally feasible strategies for the determination of the work distribution following a process undergone by a system. In the quantum regime, the concept of work done by or on a system needs to be reformulated [4] so as to include ab initio both the inherent non-deterministic nature of quantum dynamics and the effects of quantum fluctuations. In this sense, work acquires a meaning only as a statistical expectation value W = W P(W) dW that accounts for the possible trajectories followed by a quantum system across its evolution, as formalised by the associated work probability distribution P(W) = n,m p 0 n p τ m|n δ W − ( m − n ) . In order to understand this expression, let us consider a quantum system initially at equilibrium at temperature T and undergoing a quantum process that changes its Hamiltonian asĤ(0) →Ĥ(τ) within a time period τ. Then, p 0 n is the probability to find the system in the eigenstate |n(0) ofĤ(0) (with energy n ) at the start of the protocol, while p τ m|n = | m(τ)|Û|n(0) | 2 is the conditional probability to find it in the eigenstate |m(τ) ofĤ(τ) (with energy m ) if it was in |n(0) at t = 0 and evolved under the action of the propagatorÛ. P(W) encompasses the statistics of the initial state (given by p 0 n ) and the fluctuations arising from quantum measurement statistics (given by p τ m|n ). One can define a backward process that, starting from the equilibrium state of the system associated withĤ(τ) and temperature T , implements the protocolĤ(τ) →Ĥ(0) and thus inverting the control sequence of the ...

Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.

Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored to the particular dynamics whose parameters are being estimated. Here we consider a novel framework where quantum estimation is performed in an interferometric configuration, using bipartite probe states prepared when only the spectrum of the generating Hamiltonian is known. We introduce a figure of merit for the scheme, given by the worst-case precision over all suitable Hamiltonians, and prove that it amounts exactly to a computable measure of discord-type quantum correlations for the input probe. We complement our theoretical results with a metrology experiment, realized in a highly controllable room-temperature nuclear magnetic resonance setup, which provides a proof-of-concept demonstration for the usefulness of discord in sensing applications. Discordant probes are shown to guarantee a nonzero phase sensitivity for all the chosen generating Hamiltonians, while classically correlated probes are unable to accomplish the estimation in a worst-case setting. This work establishes a rigorous and direct operational interpretation for general quantum correlations, shedding light on their potential for quantum technology. All quantitative sciences benefit from the spectacular developments in high-accuracy devices, such as atomic clocks, gravitational wave detectors, and navigation sensors. Quantum metrology studies how to harness quantum mechanics to gain precision in estimating quantities not amenable to direct observation [1][2][3][4][5]. The phase estimation paradigm with measurement schemes based on an interferometric setup [6] encompasses a broad and relevant class of metrology problems, which can be conveniently cast in terms of an input-output scheme [1]. An input probe state ρ AB enters a two-arm channel, in which the reference subsystem B is unaffected while subsystem A undergoes a local unitary evolution, so that the output density matrix can be written as ρ, where φ is the parameter we wish to estimate and H A is the local Hamiltonian generating the unitary dynamics. Information on φ is then recovered through an estimator functionφ constructed upon possibly joint measurements of suitable dependent observables performed on the output ρ φ AB . For any input state ρ AB and generator H A , the maximum achievable precision is determined theoretically by the quantum Cramér-Rao bound [3]. Given repetitive interrogations via ν identical copies of ρ AB , this fundamental relation sets a lower limit to the mean square error Var ρ φ AB ðφÞ that measures the statistical distance betweenφ and φ, Var ρ φ AB ðφÞ ≥ ½νFðρ AB ; H A Þ −1 , where F is the quantum Fisher information (QFI) [7], which quantifies how much information about φ is encoded in ρ φ AB . The inequality is asymptotically tight as ν → ∞, provided the most informative quantum measurement is carried out at the output stage. Using this quantity as a figu...

Developments in the thermodynamics of small quantum systems envisage non-classical thermal machines. In this scenario, energy fluctuations play a relevant role in the description of irreversibility. We experimentally implement a quantum heat engine based on a spin-1/2 system and nuclear magnetic resonance techniques. Irreversibility at microscope scale is fully characterized by the assessment of energy fluctuations associated with the work and heat flows. We also investigate the efficiency lag related to the entropy production at finite time. The implemented heat engine operates in a regime where both thermal and quantum fluctuations (associated with transitions among the instantaneous energy eigenstates) are relevant to its description. Performing a quantum Otto cycle at maximum power, the proof-of-concept quantum heat engine is able to reach an efficiency for work extraction (η ≈ 42%) very close to its thermodynamic limit (η = 44%).

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.