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arXiv:1201.0663 · Physical Review Letters

Relativistic Motion Generates Quantum Gates and Entanglement Resonances

David Edward Bruschi, Andrzej Dragan, Antony R. Lee, Ivette Fuentes, Jorma Louko

Published Aug 27, 2013• 42 citations
arXivHTMLPDF

Abstract

We show that the relativistic motion of a quantum system can be used to generate quantum gates. The nonuniform acceleration of a cavity is used to generate well-known two-mode quantum gates in continuous variables. Observable amounts of entanglement between the cavity modes are produced through resonances that appear by repeating periodically any trajectory.

DOI
10.1103/physrevlett.111.090504

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Comment on "Towards universal quantum computation through relativistic motion"

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The work reported in arXiv:1311.5619v1 proposes to produce continuous-variable cluster states through relativistic motion of cavities. This proposal does not produce the states claimed by the authors. The states actually produced are in general not known to be useful for measurement-based quantum computation.

arXiv:1312.6188•Dec 21, 2013•1 citation
We show that the relativistic motion of a quantum system can be used to generate quantum gates. The nonuniform acceleration of a cavity is used to generate well-known two-mode quantum gates in continuous variables. Observable amounts of entanglement between the cavity modes are produced through resonances that appear by repeating periodically any trajectory.
We show that mode-mixing quantum gates can be produced by non-uniform relativistic acceleration. Periodic motion in cavities exhibits a series of resonant conditions producing entangling quantum gates between different frequency modes. The resonant condition associated with particle creation is the main feature of the dynamical Casimir effect which has been recently demonstrated in superconducting circuits. We show that a second resonance, which has attracted less attention since it implies negligible particle production, produces a beam splitting quantum gate leading to a resonant enhancement of entanglement which can be used as the first evidence of acceleration effects in mechanical oscillators. We propose a desktop experiment where the frequencies associated with this second resonance can be produced mechanically.
We analyse particle creation and mode mixing for a quantum field in an accelerated cavity, assuming small accelerations but allowing arbitrary velocities, travel times and travel distances, and in particular including the regime of relativistic velocities. As an application, we identify a desktop experimental scenario where the mode mixing resonance frequency in linear sinusoidal motion or in uniform circular motion is significantly below the particle creation resonance frequencies of the Dynamical Casimir Effect, and arguably at the threshold of current technology. The mode mixing acts as a beamsplitter quantum gate, experimentally detectable not only via fluxes or particle numbers but also via entanglement generation.
We demonstrate the presence of genuine multipartite entanglement between the modes of quantum fields in nonuniformly moving cavities. The transformations generated by the cavity motion can be considered as multipartite quantum gates. We present two setups for which multimode entanglement can be generated for bosons and fermions. As a highlight we show that the genuine bosonic multipartite correlations can be resonantly enhanced. Our results provide fundamental insights into the structure of Bogoliubov transformations and suggest strong links between quantum information, quantum fields in curved spacetimes and gravitational analogues by way of the equivalence principle.
We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.