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 ...

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.

One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like or a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system. One of the most striking departure from the classical lines of thought is the double-slit experiment with a single quantum (from here now named qubit for simplicity). This experiment, which is an example of Bohr's complementarity principle, tells us that we have to choose either to observe interference fringes (wave-like behaviour) or to know which path has been taken by the qubit (particlelike behaviour). This fact, that has been experimentally verified in many different contexts [1], means that these two knowledges (wave-like and particle-like behaviour) are mutually exclusive.A possible realization of this experiment is the singlequbit Mach-Zehnder interferometer, schematically shown in Fig. 1. After crossing the first beam splitter, BS 1 , the qubit is in a coherent superposition state of been taken both paths a and b at the same time. The second beam splitter, BS 2 , if present, recombines the qubit paths that is, then, detected by D a or D b . If we perform this experiment by varying the phase shift θ between the two paths, the result will be an interference pattern in the probability of the qubit detection by D a or D b , indicating that the it behaves like a wave (for α = π). However, if we remove BS 2 (α = 0), the interference between both paths disappears and the particle character of the qubit is observed.An important feature of classical complementarity experiment is the fact that, we can only say something about the behaviour of the system (particle or wave) after the measurement has been carried out. We then must choose beforehand what phenomenon we want to observe. This means that the two experimental arrangements are complementary. This characteristics, which is the essence of Bohr's principle, led Wheeler to formu- late his delayed-choice gedanken experiment [2]. Wheeler speculated whether the qubit could "know", before entering in the interferometer, wha...

Non-classical correlations play a crucial role in the development of quantum information science. The recent discovery that non-classical correlations can be present even in separable (unentangled) states has broadened this scenario. This generalized quantum correlation has been increasing relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the suddenchange phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to a Gibbs ensemble.

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism.

In this paper, we describe a quantum state tomography method based on global rotations of the spin system which, together with a coherence selection scheme, enables the complete density matrix reconstruction. The main advantage of this technique, in respect to previous proposals, is the use of much shorter rf pulses, which decreases significantly the time necessary for algorithm quantum state tomography. In this case, under adequate experimental conditions, the rf pulses correspond to simple spatial rotations of the spin states, and its analytical description is conveniently given in the irreducible tensor formalism. Simulated results show the feasibility of the method for a single spin 72 nucleus. As an experimental result, we exemplify the application of this method by tomographing the steps during the implementation of the Deutsch algorithm. The algorithm was implemented in a (23)Na quadrupole nucleus using the strongly modulated pulses technique. We also extended the tomography method for a 3-coupled homonuclear spin 12 system, where an additional evolution under the internal Hamiltonian is necessary for zero order coherences evaluation.

We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.