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One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is neither. The resolution to this paradox is to recognize that global unitary evolution of a multi-partite quantum state causes the state of local subsystems to evolve towards maximum-entropy states. In this work, we experimentally demonstrate this effect in linear quantum optics by simultaneously showing the convergence of local quantum states to a generalized Gibbs ensemble constituting a maximum-entropy state under precisely controlled conditions, while introducing an efficient certification method to demonstrate that the state retains global purity. Our quantum states are manipulated by a programmable integrated quantum photonic processor, which simulates arbitrary non-interacting Hamiltonians, demonstrating the universality of this phenomenon. Our results show the potential of photonic devices for quantum simulations involving non-Gaussian states. The emergence of relaxation in unitarily evolving systems can be seen as a paradox, but not once the distinction between local and global dynamics is considered. Here, the authors use photons in an integrated optical interferometer to show that, for a system evolving unitarily on a global level, single-mode measurements converge to those of a thermal state. [ABSTRACT FROM AUTHOR]

Signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or any harmonic oscillator state, must introduce noise. This linear amplification noise prevents perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the mechanism preventing the increase of entanglement via local operations. Non-deterministic versions of ideal cloning and local entanglement increase (distillation) are allowed, suggesting the possibility of non-deterministic noiseless linear amplification. Here we introduce, and experimentally demonstrate, such a noiseless linear amplifier for quantum states of the optical field, and use it for distillation of field-mode entanglement. This simple but powerful circuit enables practical devices for enhancing quantum technologies. The idea of noiseless amplification unifies approaches to cloning and distillation, and will find applications in quantum metrology and communications. [ABSTRACT FROM AUTHOR]