Abstract
We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing entanglement entropy ΔS, by a product state, and we show how to construct modes achieving this minimal energy cost. Thus, we obtain a protocol independent lower bound on the extraction of pure state entanglement from quadratic systems. Due to their generality, our results apply to a large range of physical systems, as we discuss with examples.
Highlights
Entanglement is a hallmark of quantum theory: On a fundamental level, its very existence has deep implications for our understanding of nature, e.g., as pertaining to its realism and localism [1–6]
Our proof follows three steps: 1. Splitting the problem into two parts In section 3.2, we show that the problem of finding the minimal energy cost can be broken up into first solving the problem for a system of two modes, and optimizing how to embed these two modes used for entanglement extraction into the larger system
We have found the minimal energy cost of extracting a pair of entangled partner modes from the ground state of a quadratic Hamiltonian, and we have characterized the modes which achieve this minimal energy cost
Summary
Entanglement is a hallmark of quantum theory: On a fundamental level, its very existence has deep implications for our understanding of nature, e.g., as pertaining to its realism and localism [1–6]. The extraction of entanglement from a system’s unique ground state is inevitably associated with an energy increase injected into the system when changing its state This interplay of entanglement extraction and energy cost is relevant with respect to potential implementations and quantum thermodynamics but, connects to quantum field theory on curved spacetimes. We present a first result in the direction initiated by [48] which applies to large classes of systems of physical interest: We study the extraction of entanglement from the ground state of bosonic and fermionic modes governed by a quadratic Hamiltonian. 51], mostly in the context of bosonic quantum field theory We generalize this construction, such that it applies to any bosonic or fermionic pure Gaussian state.
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