We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order Rényi entropy to simulate the engine. We also study the information-work efficiency of the Szilard engine as a function of the system parameters. The efficiency is defined as the ratio of the extractable work averaged over the measurement angle and the erasure work, which is proportional to the information stored in the system. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. The extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir. The efficiency mostly has a similar behavior with the extractable quantum work evolution. However information-work efficiency decreases with temperature, while the quantity of the extractable work increases.
We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order Rényi entropy to simulate the engine. We also study the information-work efficiency of the Szilard engine as a function of the system parameters. The efficiency is defined as the ratio of the extractable work averaged over the measurement angle and the erasure work, which is proportional to the information stored in the system. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. The extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir. The efficiency mostly has a similar behavior with the extractable quantum work evolution. However information-work efficiency decreases with temperature, while the quantity of the extractable work increases.
We investigate the influence of the seed of measurement on the performance of a Szilard engine based on a two-mode Gaussian state evolving in a noisy channel. Quantum work is extracted by performing a positive operator-valued measurement (POVM) on one of the two modes, after which this mode reaches equilibrium with the environment. As the seed of measurement, we use a single-mode squeezed thermal state. We employ the Markovian Kossakowski-Lindblad master equation to determine the evolution in time of the considered open system and the quantum work is defined based on the Rényi entropy of order 2. We show that the extracted quantum work and information-work efficiency strongly depend on the characteristic parameters of the system (frequency, average thermal photons number, and squeezing), the noisy channel (temperature and squeezing of the bath), and the seed of measurement (average thermal photons number and strength of the measurement).
The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.
We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.
The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically study the basic physical properties of both fermion and boson SQSZEs in a low-temperature approximation. We give the analytic formulation of the total work. For the fermion SQSZE, the work might be absorbed from the environment, and the change rate of the work with temperature exhibits periodicity and even-odd oscillation, which is a generalization of a spinless QSZE. It is interesting that the average absorbed work oscillates regularly and periodically in a large-number limit, which implies that the average absorbed work in a fermion SQSZE is neither an intensive quantity nor an extensive quantity. The phase diagrams of both fermion and boson SQSZEs give the SQSZE doing positive or negative work in the parameter space of the temperature and the particle number of the system, but they have different behaviors because the spin degrees of the fermion and the boson play different roles in their configuration states and corresponding statistical properties. The critical temperature of phase transition depends sensitively on the particle number. By using Landauer's erasure principle, we give the erasure work in a thermodynamic cycle, and we define an efficiency (we refer to it as information-work efficiency) to measure the engine's ability of utilizing information to extract work. We also give the conditions under which the maximum extracted work and highest information-work efficiencies for fermion and boson SQSZEs can be achieved.
Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to 0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit, was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98, 15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.
The connections between thermodynamics and quantum information processing are of paramount importance. Here, we address a bipartite entanglement via extracted work in a cavity magnomechanical system contained inside an yttrium iron garnet (YIG) sphere. The photons and magnons interact through an interaction between magnetic dipoles. A magnetostrictive interaction, analogous to radiation pressure, couple's phonons and magnons. The extracted work was obtained through a device similar to the Szilárd engine. This engine operates by manipulating the photon-magnon as a bipartite quantum state. We employ logarithmic negativity to measure the amount of entanglement between photon and magnon modes in steady and dynamical states. We explore the extracted work, separable work, and maximum work for squeezed thermal states. We investigate the amount of work extracted from a bipartite quantum state, which can potentially determine the degree of entanglement present in that state. Numerical studies show that entanglement, as detected by the extracted work and quantified by logarithmic negativity, is in good agreement. We show the reduction of extracted work by a second measurement compared to a single measurement. Also, the efficiency of the Szilard engine in steady and dynamical states is investigated. We hope this work is of paramount importance in quantum information processing.