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Understanding how macroscopic systems exhibit irreversible thermal behavior has been a long-standing challenge, first brought to prominence by Boltzmann. Recent advances have established rigorous conditions for isolated quantum systems to equilibrate to a maximum entropy state, contingent upon weak assumptions. These theorems, while powerful, apply for a sudden quench. However, natural processes involve finite-time perturbations or quenches, which raises a crucial question: Can these systems still equilibrate under more realistic, finite-time dynamics? In this work, we extend the established results to account for finite-time quenches, demonstrating that even under finite-time perturbations, the system will equilibrate provided it populates many significant energy levels. While the mathematical proof is more intricate than in the instantaneous case, the physical conclusion remains the same: sufficient perturbation leads to equilibration. Our results provide a broader and more physically realistic framework for understanding thermalization in isolated quantum systems, Comment: comments are welcome

We propose a procedure to identify and classify genuine tripartite entanglement in pure 3-qubit states via the Activated Bipartite Entanglement (ABE), which is defined here as the difference between the Entanglement of Assistance and the Entanglement of Formation. We show that for pure states belonging to one of the two inequivalent classes of genuine tripartite entanglement, i.e., GHZ or W states, the ABE is always greater than zero. For separable and biseparable states it is always null. In addition, our approach is capable to distinguish between genuine tripartite entangled states, those belonging to the GHZ class from those belonging to the W class. We also present an experimental proposal, by using linear optical circuits and internal degrees of freedom of a single photon, to measure the ABE and to verify the characterization via activated entanglement. The circuit simulation shows an excellent agreement with theoretical prediction for a wide class of GHZ and W states., Comment: Improved version, 6 pages, 4 figures

The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Phys. Rev. Lett 88, 017901 (2002)] is difficult to compute even for the simplest case of two-qubits systems. Alternative formulations have been developed to address this drawback, such as the geometric measure of quantum discord [Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [Phys. Rev. Lett 110, 240402 (2013)] that can be evaluated in closed form for some quantum systems, such as two-qubit systems. We show here that these two measures of quantum discord are equivalent for 2 x D dimensional bipartite quantum systems. By considering the relevant example of N00N states for phase estimation in lossy environments, we also show that both metrics of quantum discord quantify the decrease of quantum Fisher information of the phase estimation protocol. Given their ease of computation in 2 x D bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord., Comment: 7 pages - 4 figures

The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to arbitrary accuracy with a finite sequence of fundamental operations from a universal set of gates. Inspired by this decomposition, we present a quantum channel simulator capable of implementing any completely positive trace-preserving map. Our realization consists of one ancillary qubit, encoded in the transverse mode of a laser beam (orbital degree of freedom), one qubit system, encoded in its polarization (spin), one spin-orbit CNOT gate and four single-qubit operations performed with prisms and polarization components. Our results describe the implementation of arbitrary single-qubit channels on the photon polarization using the transverse mode as the ancillary qubit., Comment: 13 pages, 15 figures

The use of the adiabatic approximation in practical applications, as in adiabatic quantum computation, demands an assessment of the errors made in finite-time evolutions. Aiming at such scenarios, we derive bounds relating error and evolution time in the adiabatic approximation that go beyond typical scaling relations. Using the Adiabatic Perturbation Theory, we obtain leading-order expressions valid for long evolution time $T$, while explicitly determining the shortest time $T$ and the largest error $\varepsilon$ for which they are valid. In this validity regime, we can make clear and precise statements about the evolution time needed to reach a given error and vice-versa. As an example of practical importance, we apply these results to the adiabatic search, and obtain for the first time an error-run-time trade-off relation that fully reproduces the discrete-Grover-search scaling. We also pioneer the obtention of tight numerical values for $\varepsilon$ and $T$ under the error-reducing strategy ``boundary cancelation''., Comment: Main text 16 pages, 26 pages total (with appendix), 3 figures

We introduce both a theoretical and an experimental scheme for simulating a quantum thermal engine through an all-optical approach, with the behavior of the working substance and the thermal reservoirs implemented via internal degrees of freedom of a single photon. By using the polarization and propagation path, we encode two quantum bits and then implement the thermodynamical steps of an Otto cycle. To illustrate the feasibility of our proposal, we experimentally realize such simulation through an intense laser beam, evaluating heat and work at each individual step of the thermodynamical cycle. In addition, from the analysis of the entropy production during the entire cycle, we can study the amount of quantum friction produced in the Otto cycle as a function of the difference of temperature between hot and cold reservoirs. Our paper constitutes, therefore, an all-optical-based thermal machine simulation and opens perspectives for other optical simulations in quantum thermodynamics., Comment: 9 pages, 5 figures

We experimentally observed the violation of Kujula-Dzhafarov noncontextuality inequalities by non-separable spin-orbit laser modes. Qubits are encoded on polarization and transverse modes of an intense laser beam. A spin-orbit non-separable mode was produced by means of a radial polarization converter (S-plate). The results show that contextuality can be investigated by using spin-orbit modes in a simple way, corroborating recent works stating that such system can emulate single-photon experiments. Additionally, an improvement in the non-separable mode preparation allowed us to observe a greater violation of the Clauser-Horne-Shimony-Holt inequality for such system. The results are in very good agreement with the theoretical predictions of quantum mechanics., Comment: 8 pages, 4 Figures

We propose an all-optical experiment to quantify non-Markovianity in an open quantum system through quantum coherence of a single quantum bit. We use an amplitude damping channel implemented by an optical setup with an intense laser beam simulating a single-photon polarization. The optimization over initial states required to quantify non-Markovianity is analytically evaluated. The experimental results are in a very good agreement with the theoretical predictions., Comment: 5 pages, 4 figures

We investigate the generation of entanglement between two non interacting qubits coupled to a common reservoir. An experimental setup was conceived to encode one qubit on the polarization of an optical beam and another qubit on its transverse mode. The action of the reservoir is implemented as conditional operations on these two qubits, controlled by the longitudinal path as an ancillary degree of freedom. An entanglement witness and the two-qubit concurrence are easily evaluated from direct intensity measurements showing an excellent agreement with the theoretical prediction., Comment: 7 pagea, 5 figures