Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy

Abstract

The two-time measurement scheme is well studied in the context of quantum fluctuation theorem. However, it becomes infeasible when the random variable determined by a single measurement trajectory is associated with the von-Neumann entropy of the quantum states. We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production by proposing an information production distribution based on the quantum cross entropy. The derived equality further enables one to explore the roles of the quantum cross entropy in quantum communications, quantum machine learning and quantum thermodynamics.

arXiv commentv2: We removed the results of two-time measurement scheme, and added the relations of our main result of the one-time measurement scheme to the cost function of quantum autoencoder and maximum available work theorem

References in corpus (60)

• Quantum Computing in the NISQ era and beyond
• A nonequilibrium equality for free energy differences
• Variational Quantum Algorithms
• An Introduction to Variational Autoencoders
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Steady State Thermodynamics of Langevin Systems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Quantum autoencoders for efficient compression of quantum data
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Quantum generalisation of feedforward neural networks
• Variational quantum algorithms for discovering Hamiltonian spectra
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Duality Between Smooth Min- and Max-Entropies
• Fluctuation theorem for currents in open quantum systems
• Quantum technologies need a Quantum Energy Initiative
• No-go theorem for the characterisation of work fluctuations in coherent quantum systems
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Quantum autoencoders to denoise quantum data
• Quantum work and the thermodynamic cost of quantum measurements
• Variational Quantum Fidelity Estimation
• Anomaly detection in high-energy physics using a quantum autoencoder
• Fluctuation theorems for quantum processes
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning
• Quantum work relations and response theory
• Quantum fluctuation theorems beyond two-point measurements
• Holevo's bound from a general quantum fluctuation theorem
• A quasiprobability distribution for heat fluctuations in the quantum regime
• The quantum-classical correspondence principle for work distributions
• Jarzynski equality for quantum stochastic maps
• Non-equilibrium equalities with unital quantum channels
• Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Energetic cost of Hamiltonian quantum gates
• Realization of a quantum autoencoder for lossless compression of quantum data
• Noise-Assisted Quantum Autoencoder
• Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme
• Fluctuation theorems from Bayesian retrodiction
• Fundamental limits on quantum dynamics based on entropy change
• From quantum speed limits to energy-efficient quantum gates
• Experimental test of exchange fluctuation relations in an open quantum system
• Work as an external quantum observable and an operational quantum work fluctuation theorem
• Quantum fluctuation theorem to benchmark quantum annealers
• Quantum autoencoders with enhanced data encoding
• Quantum Error Correction with Quantum Autoencoders
• Kibble-Zurek scaling of the irreversible entropy production
• Experimental test of fluctuation relations for driven open quantum systems with an NV center
• Towards a unified approach to information-disturbance tradeoffs in quantum measurements
• Two-point measurement of entropy production from the outcomes of a single experiment with correlated photon pairs
• Jarzynski equality for conditional stochastic work
• A quantum fluctuation theorem for any Lindblad master equation
• Subnormalized states and trace-nonincreasing maps
• Information loss and run time from practical application of quantum data compression

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• Exchange fluctuation theorems for strongly interacting quantum pumps
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