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arXiv:1407.2442 · Physical Review A

Quantum macroscopicity versus distillation of macroscopic superpositions

Benjamin Yadin, Vlatko Vedral

Published Aug 28, 2015• 18 citations
arXivHTMLPDF

Abstract

We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are.

DOI
10.1103/physreva.92.022356

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We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are.
The tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC) are studied. For the former, known as common randomness (CR) distillation, two novel lower bounds on the "distillable common randomness", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50: 3047-3061, 2004]. For the latter, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in "making coherent" the proposed CR distillation protocols and recycling of resources [Devetak, Harrow and Winter, IEEE Trans. Inf. Theory 54:4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65:5945-5958, 2019], which is based on a combinatorial approach to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation. Full details in the long version [1].
The multipartite Greenberger-Horne-Zeilinger (GHZ) state is a paradigmatic example of a highly entangled multipartite state with distinct quantum features. However, the GHZ state is very sensitive to generic decoherence processes, where its quantum features and, in particular, its entanglement diminish rapidly, thereby hindering possible practical applications. In this paper, we discuss GHZ-like quantum states with a block-local structure and show that they exhibit a drastically increased stability against noise for certain choices of block-encoding, thereby extending results of [Phys. Rev. Lett. 106, 110402 (2011)]. We analyze in detail the decay of the interference terms, the entanglement in terms of distillable entanglement, and negativity as well as the notion of macroscopicity as measured by the so-called index qqq and provide general bounds on these quantities. We focus on an encoding where logical qubits are themselves encoded as GHZ states, which leads to so-called concatenated GHZ (C-GHZ) states. We compare the stability of C-GHZ states with other types of encodings, thereby showing the superior stability of the C-GHZ states. Analytic results are complemented by numerical studies, where tensor network techniques are used to investigate the quantum properties of multipartite entangled states under the influence of decoherence.
One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to Schr\"odinger's cat thought experiment. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of macroscopic quantumness relies on states such as the Greenberger-Horne-Zeilinger (GHZ) or the NOON state. Here we take a first-principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and require the quantumness to be collective and macroscopic. To this end, we introduce macroscopic coherence which is the coherence between macroscopically distinct quantum states. We construct a measure that quantifies how global and collective the coherence of the state is. Our work also provides a first-principle way to derive well-established states like the GHZ and the NOON state as the states that maximize our measure. Our approach paves the way towards a better understanding of the quantum-to-classical transition.
I show relations between superposition of macroscopically distinct states and entanglement. These relations lead to the important conclusion that if a state includes superposition of macroscopically distinct states, the state also includes large multipartite entanglement in terms of several measures. Such a multipartite entanglement property also suggests that if a state includes superposition of macroscopically distinct states, a measurement on a single particle drastically changes the state of macroscopically many other particles, as in the case of the NNN-qubit Greenberger- Horne-Zeilinger state.