Gaussian work extraction from random Gaussian states is nearly impossible

Abstract

Quantum thermodynamics can be naturally phrased as a theory of quantum state transformation and energy exchange for small-scale quantum systems undergoing thermodynamical processes, thereby making the resource theoretical approach very well suited. A key resource in thermodynamics is the extractable work, forming the backbone of thermal engines. Therefore it is of interest to characterize quantum states based on their ability to serve as a source of work. From a near-term perspective, quantum optical setups turn out to be ideal test beds for quantum thermodynamics; so it is important to assess work extraction from quantum optical states. Here, we show that Gaussian states are typically useless for Gaussian work extraction. More specifically, by exploiting the ``concentration of measure'' phenomenon, we prove that the probability that the Gaussian extractable work from a zero-mean energy-bounded multimode random Gaussian state is nonzero is exponentially small. This result can be thought of as an $\epsilon$-no-go theorem for work extraction from Gaussian states under Gaussian unitaries, thereby revealing a fundamental limitation on the quantum thermodynamical usefulness of Gaussian components.

arXiv comment7+8 pages, 2 figures, close to the published version

References in corpus (42)

• Gaussian Quantum Information
• Artificial Brownian motors: Controlling transport on the nanoscale
• Quantum computation over continuous variables
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Fundamental limitations for quantum and nano thermodynamics
• A single-atom heat engine
• The second laws of quantum thermodynamics
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Squeezing as an irreducible resource
• High-power collective charging of a solid-state quantum battery
• Work extraction and thermodynamics for individual quantum systems
• Gaussian transformations and distillation of entangled Gaussian states
• Experimental demonstration of quantum effects in the operation of microscopic heat engines
• Quantum Equivalence and Quantum Signatures in Heat Engines
• The Real Symplectic Groups in Quantum Mechanics and Optics
• Aspects of generic entanglement
• A No-Go Theorem for Gaussian Quantum Error Correction
• Quantum absorption refrigerator with trapped ions
• An introductory review of the resource theory approach to thermodynamics
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Precision and Work Fluctuations in Gaussian Battery Charging
• An all-optical nanomechanical heat engine
• Generalized Laws of Thermodynamics in the Presence of Correlations
• Time-resolved observation of thermalization in an isolated quantum system
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Passivity and practical work extraction using Gaussian operations
• Thermodynamics as a Consequence of Information Conservation
• Heat-Bath Algorithmic Cooling with correlated qubit-environment interactions
• Generic Entanglement and Standard Form for N-mode Pure Gaussian States
• Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy
• Teleportation fidelities of squeezed states from thermodynamical state space measures
• Typical entanglement for Gaussian states
• Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Partial order on passive states and Hoffman majorization in quantum thermodynamics
• A quantum de Finetti theorem in phase space representation
• Invariant measures on multimode quantum Gaussian states