The Jarzynski equality relates the free-energy di erence between two equilibrium states to the work done on a system through far-from-equilibrium processes-a milestone that builds on the pioneering work of Clausius and Kelvin. Although experimental tests of the equality have been performed in the classical regime, the quantum Jarzynski equality has not yet been fully verified owing to experimental challenges in measuring work and work distributions in a quantum system. Here, we report an experimental test of the quantum Jarzynski equality with a single 171 Yb + ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. We then apply a laser-induced force to the projected energy eigenstate and find transition probabilities to final energy eigenstates after the work is done. By varying the speed with which we apply the force from the equilibrium to the far-from-equilibrium regime, we verify the quantum Jarzynski equality in an isolated system. T here is increasing interest in non-equilibrium dynamics at the microscopic scale, crossing over quantum physics, thermodynamics and information theory as the experimental control and technology at such a scale have been developing rapidly. Most of the principles in non-equilibrium processes are represented in the form of inequalities, as seen in the example of the maximum work principle, W − F ≥ 0, where the average work W is equal to the free-energy difference F only in the case of the equilibrium process. In close-to-equilibrium processes, the fluctuation-dissipation theorem is valid and connects the average dissipated energy W diss ≡ W − F and the fluctuation of the system σ 2 /2k B T . Here σ is the standard deviation of the work distribution, T is the initial temperature of the system in thermal equilibrium and k B is the Boltzmann constant. Beyond the nearequilibrium regime, no exact results were known until Jarzynski found a remarkable equality 1 that relates the free-energy difference to the exponential average of the work done on the system:The Jarzynski equality (1) is satisfied irrespective of the protocols of varying parameters of the system even when the driving is arbitrarily far from equilibrium. The relation enables us to experimentally determine F of a system by repeatedly performing work at any speed. Experimental tests of the classical Jarzynski equality and its relation to the Crooks fluctuation theorem 2 have been successfully performed in various systems 3-12 .In classical systems, work can be obtained by measuring the force and the displacement, and then integrating the force over the displacement during the driving process. In the quantum regime, however, as a result of Heisenberg's uncertainty principle, we cannot determine the position and the momentum simultaneously-thus invalidating the concepts of force and displacement. Instead of measuring these classical observables, it is necessary to carry out projective measurements over the energy eigenstates to determine the work d...

A long-time quantum memory capable of storing and measuring quantum information at the single-qubit level is an essential ingredient for practical quantum computation and com-munication [1,2]. Recently, there have been remarkable progresses of increasing coherence time for ensemble-based quantum memories of trapped ions [3,4], nuclear spins of ionized donors [5] or nuclear spins in a solid [6]. Until now, however, the record of coherence time of a single qubit is on the order of a few tens of seconds demonstrated in trapped ion systems [7][8][9]. The qubit coherence time in a trapped ion is mainly limited by the increasing magnetic field fluctuation and the decreasing state-detection efficiency associated with the motional heating of the ion without laser cooling [10,11]. Here we report the coherence time of a single qubit over 10 minutes in the hyperfine states of a 171 Yb + ion sympathetically cooled by a 138 Ba + ion in the same Paul trap, which eliminates the heating of the qubit ion even at room temperature. To reach such coherence time, we apply a few thousands of dynamical decoupling pulses to suppress the field fluctuation noise [5,6,[12][13][14][15][16]. A long-time quantum memory demonstrated in this experiment makes an important step for construction of the memory zone in scalable quantum computer architectures [17,18] or for ion-trap-based quantum networks [2,19,20]. With further improvement of the coherence time by techniques such as magnetic field shielding and increase of the number of qubits in the quantum memory, our demonstration also makes a basis for other applications including quantum money [21,22].The trapped ion system constitutes one of the leading candidates for the realization of large-scale quantum computers [1]. It also provides a competitive platform for the realization of quantum networks which combines long-distance quantum communication with local quantum computation [2]. One scalable architecture for iontrap quantum computer is to divide the system into operation and memory zones and to connect them through ion shuttling [17,18]. For this architecture, the basic unit of operation zone has been demonstrated [23,24]. As the size of the system scales up, the needed storage time of the qubits in the memory zone will correspondingly increase. To keep the qubit error rates below a certain threshold for fault-tolerant computation, it is crucial to extend the coherence time of qubits. For the quantum network based on probabilistic ion-photon mapping [25], the basic units of ion-photon and ion-ion entanglement have been demonstrated [26][27][28]. The required coherence time of qubits increases in this approach as the size of the system grows. A long-time quantum memory is therefore important for both quantum computation and communication [2,29].For trapped ion qubits, the main noise is not relaxation with time T 1 but instead dephasing with time T * 2 induced by fluctuation of magnetic fields. The current records of single-qubit coherence time in trapped ion systems are around tens of se...

Realizing a long coherence time quantum memory is a major challenge of current quantum technology. Until now, the longest coherence-time of a single qubit was reported as 660 s in a single 171Yb+ ion-qubit through the technical developments of sympathetic cooling and dynamical decoupling pulses, which addressed heating-induced detection inefficiency and magnetic field fluctuations. However, it was not clear what prohibited further enhancement. Here, we identify and suppress the limiting factors, which are the remaining magnetic-field fluctuations, frequency instability and leakage of the microwave reference-oscillator. Then, we observe the coherence time of around 5500 s for the 171Yb+ ion-qubit, which is the time constant of the exponential decay fit from the measurements up to 960 s. We also systematically study the decoherence process of the quantum memory by using quantum process tomography and analyze the results by applying recently developed resource theories of quantum memory and coherence. Our experimental demonstration will accelerate practical applications of quantum memories for various quantum information processing, especially in the noisy-intermediate-scale quantum regime.

We experimentally observed state-independent violations of Kochen-Specker inequalities for the simplest indivisible quantum system manifesting quantum contextuality, a three-level (qutrit) system. We performed the experiment with a single trapped 171 Yb + ion, by mapping three ground states of the 171 Yb + ion to a qutrit system and carrying out quantum operatations by applying microwaves resonant to the qutrit transition frequencies. Our results are free from the detection loophole and cannot be explained by the non-contextual hidden variable models. 03.65.Ud, 37.10.Ty, 32.50.+d It is a long-standing problem whether the nature of physical system would be completely described by quantum mechanics. In classical views the measurement outcomes on physical properties are non-contextual, i.e., predetermined independently of their own and other simultaneous compatible measurements, while quantum mechanics is contextual. Kochen, Specker and Bell proved that quantum mechanics and any non-contextual classical theory are in conflict [1,2], deeply rooted in the essence of quantum mechanics regardless of states of the system. The original logical proof has been formulated to experimentally testable inequalities, called Kochen-Specker (KS) inequalities. The Bell's inequalities that hold for classical theories with local hidden variables can be considered as a special type of KS inequalities, where the contextuality is presented by non-locality. While Bell's inequalities can be violated by special entangled states in space-like separation, the violation of KS inequalities could be observed by any quantum state in a system with dimension d ≥ 3. For cases where d ≥ 4, KS inequalities were proposed [3][4][5] and demonstrated in both a state-dependent [6-8] and a state-independent manner [9][10][11]. For the smallest case d = 3, the state-dependent inequality was developed [12] and tested with a photon system [13]. Lately, the state-independent inequality was found [14,15] and the violations were informed with also a photon system [16]. However, these experimental demonstrations are open to the detection loophole. Here we report the experimental results of a single three-level atomic ion that are in conflict with non-contextual classical theories. The experimental violations of KS inequalities are observed independently of entanglement or superposition of the states and confirm the quantum contextuality at the most simple and fundamental level without the fair sampling assumption.In noncontextual classical models, values of an observable are determined by only a hidden variable independently of the measurement context, i.e., set of mutually compatible observables measured in a single experimental setting. The observables are compatible if their results are not dependent on the order of measurements. Kochen and Specker showed that any quantum state in larger than 2 dimensions would reveal conflict with the non-contextual theories. The demonstration of Table I. the conflict in a simplest three dimensional quantum system, a qut...

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