We experimentally study the response of star-shaped clusters of initially unentangled N=4, 10, and 37 nuclear spin-1/2 moments to an inexact π-pulse sequence and show that an Ising coupling between the center and the satellite spins results in robust period-2 magnetization oscillations. The period is stable against bath effects, but the amplitude decays with a timescale that depends on the inexactness of the pulse. Simulations reveal a semiclassical picture in which the rigidity of the period is due to a randomizing effect of the Larmor precession under the magnetization of surrounding spins. The timescales with stable periodicity increase with net initial magnetization, even in the presence of perturbations, indicating a robust temporal ordered phase for large systems with finite magnetization per spin.

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We experimentally verify the Jarzynski and Wöjcik quantum heat exchange fluctuation relation by implementing the interferometric technique in liquid-state Nuclear Magnetic Resonance setup and study the exchange heat statistics between two weakly coupled spin-1/2 quantum systems. In presence of uncorrelated initial state with individual spins prepared in local Gibbs thermal states at different temperatures, the exchange fluctuation symmetry is verified for arbitrary transient time. In contrast, when the initial preparation includes correlation, the fluctuation symmetry breaks down and further leads to an apparent spontaneous flow of heat from cold to hot. Our experimental approach is general and can be systematically extended to study heat statistics for more complex out-of-equilibrium many-body quantum systems.Introduction.-Quantifying thermal and quantum fluctuations for mesoscopic and nanoscale systems are important both from fundamental and practical perspectives [1]. In the past two decades, considerable research have been devoted in developing a consistent theoretical framework to describe these fluctuations which have lead to the discovery of what is now collectively referred to as "fluctuation relations (FR)" [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. For out-ofequilibrium systems, classical or quantum, various thermodynamic observables such as work and heat are found to follow these universal relations either in the transient [5][6][7] and/or in the steady state regimes [16,17]. Apart from quantifying the probability of observing the rare events related to negative entropy production, fluctuation relations correctly describe systems residing at arbitrarily far-from-equilibrium and further serve as essential ingredient for establishing the rapidly growing field of quantum thermodynamics [19][20][21].Despite impressive theoretical progress, experimental verification of these FR's remained as a challenge in the quantum domain, primarily because of the requirement of projective measurements to construct the probability distribution function (PDF) for work/heat. In recent times, several experimental proposals have been put forward to construct such PDF [22][23][24][25][26][27][28]. Following projective measurement scheme, the first experimental success for the work fluctuation relation was achieved in an iontrap setup [29][30][31][32]. Later, this difficult projective measurement scheme was circumvented and an ancilla based Ramsey intereferometric approach was proposed [23] following which the work fluctuation relation was verified [24,25]. Further successful attempts were also made recently to study similar fluctuation relation for open systems [32].In this work, we attempt to verify the quantum version of Jarzynski and Wöjcik heat "exchange fluctuation theorem " (XFT) [7] which has not been achieved till date and this is the gap we want to fill in this work. We employ here a similar interferometric approach, as proposed for measuring work statistics, in a liquid Nuclear Magnetic Resonance ...

Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that are interacting solely via a mediator implies non-classicality of the mediator. Indeed, under certain assumptions regarding the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactions with a classical mediator. In this process the initial entanglement between any probe and the rest of the system "flows through" the classical mediator and gets localised between the probes. Here we theoretically characterise maximal entanglement gain via classical mediator and experimentally demonstrate, using liquid-state NMR spectroscopy, the optimal growth of quantum correlations between two nuclear spin qubits interacting through a mediator qubit in a classical state. We additionally monitor, i.e., dephase, the mediator in order to emphasise its classical character. Our results indicate the necessity of verifying features of the initial state if entanglement gain between the probes is used as a figure of merit for witnessing non-classical mediator. Such methods were proposed to have exemplary applications in quantum optomechanics, quantum biology and quantum gravity.