Coherence and Asymmetry Cannot be Broadcast

Abstract

In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing that this is forbidden by quantum mechanics in every finite-dimensional system. In doing so we also answer some open questions in the quantum information literature concerning the sharing of timing information of a clock and the possibility of catalysis in quantum thermodynamics. We also prove that even weaker forms of broadcasting, of whichÅberg's 'catalytic coherence' is a particular example, can only occur in the presence of infinite-dimensional reference systems. Our results set fundamental limits to the creation and manipulation of quantum coherence and shed light on the possibilities and limitations of quantum reference frames to act catalytically without being degraded. arXiv:1812.08214v2 [quant-ph]

Second law of thermodynamics for batteries with vacuum state

“…Throughout we adapt a resource-theoretic approach to quantum thermodynamics called thermal operations [27,27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. This is a wellestablished framework for studying thermodynamic processes in the quantum regime which gives the experimenter the most freedom in manipulating systems without access to external resources like coherence or asymmetry [25,[46][47][48][49], entanglement [50][51][52] or conserved quantities [53][54][55]. It is thus a convenient class of operations for deriving fundamental thermodynamic limitations.…”

Quantum thermodynamics and quantum coherence engines

“…Quantum coherence and correlations require a cost of production as they are resources [98,99], which should be adequately translated to the first and second laws of quantum thermodynamics in the case of quantum coherent or correlated systems [100]. Even catalytic use of coherence has been argued to be limited fundamentally [101,102]. By identifying quantum thermal operations and their resource theoretic descriptions, fundamental bounds on quantum information-thermal engines have been provided [103].…”

Coherence and catalysis in the Jaynes–Cummings model

“…It can be shown that coherence does not increase under strictly energy preserving operations, that is, operations that commute with the system Hamiltonian. However, by allowing correlations to build up, it is possible to put an arbitrary number of systems into approximate coherent superpositions with the help of an infinite-dimensional reference system acting as a catalyst [29,30,48] 2 . In this work, we are interested in a variation of this coherence 'catalysis' in which an optical coherent state acts as our reference system.…”