Thermodynamically optimal creation of correlations

Abstract

Correlations lie at the heart of almost all scientific predictions. It is therefore of interest to ask whether there exist general limitations to the amount of correlations that can be created at a finite amount of invested energy. Within quantum thermodynamics such limitations can be derived from first principles. In particular, it can be shown that establishing correlations between initially uncorrelated systems in a thermal background has an energetic cost. This cost, which depends on the system dimension and the details of the energy-level structure, can be bounded from below but whether these bounds are achievable is an open question. Here, we put forward a framework for studying the process of optimally correlating identical (thermal) quantum systems. The framework is based on decompositions into subspaces that each support only states with diagonal (classical) marginals. Using methods from stochastic majorisation theory, we show that the creation of correlations at minimal energy cost is possible for all pairs of three- and four-dimensional quantum systems. For higher dimensions we provide sufficient conditions for the existence of such optimally correlating operations, which we conjecture to exist in all dimensions.

arXiv comment12+16 pages, 2 figures

References in corpus (26)

• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• The Physics of Maxwell's demon and information
• Quantacell: Powerful charging of quantum batteries
• Extractable Work from Correlations
• A derivation (and quantification) of the third law of thermodynamics
• Perspective: Quantum Thermodynamics
• Generalized Laws of Thermodynamics in the Presence of Correlations
• Thermodynamic cost of creating correlations
• Correlating thermal machines and the second law at the nanoscale
• Correlations in quantum thermodynamics: Heat, work, and entropy production
• Von Neumann entropy from unitarity
• Inequalities for the Ranks of Quantum States
• Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling
• The thermodynamics of creating correlations: Limitations and optimal protocols
• Maximally and minimally correlated states attainable within a closed evolving system
• Birkhoff's polytope and unistochastic matrices, N=3 and N=4
• The structure of Renyi entropic inequalities
• Thermodynamics as a Consequence of Information Conservation
• Third Law of Thermodynamics as a Single Inequality
• Correlations as a resource in quantum thermodynamics
• Energetics of correlations in interacting systems
• Quantum Mutual Information Along Unitary Orbits
• Trade-off Between Work and Correlations in Quantum Thermodynamics
• Fluctuations of work cost in optimal generation of correlations
• Allowed and Forbidden Bipartite Correlations from Thermal States

Cited by in corpus (14)

• Ideal Projective Measurements Have Infinite Resource Costs
• Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
• Entropy-Based Formulation of Thermodynamics in Arbitrary Quantum Evolution
• Energy-Consumption Advantage of Quantum Computation
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Correlations enable lossless ergotropy transport
• Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry
• Mutual Information is not a Reliable Measure for Variations in Total Correlations
• Correlation-Enabled Energy Exchange in Quantum Systems without External Driving
• Binding energy of bipartite quantum systems: Interaction, correlations, and tunneling
• Generation of minimum energy entangled states
• Energy bounds for entangled states
• Correlations and energy in mediated dynamics
• Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems