Resource theory of quantum non-Gaussianity and Wigner negativity

Albarelli, Francesco; Genoni, Marco G.; Paris, Matteo G. A.; Ferraro, Alessandro

doi:10.1103/physreva.98.052350

Cited by 237 publications

(243 citation statements)

References 121 publications

(193 reference statements)

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“…It has been shown that nonlinearities in the form of non-Gaussian states constitute an important resource for quantum teleportation protocols [1], universal quantum computation [2,3], quantum error correction [4], and entanglement distillation [5][6][7]. This view of non-Gaussianity as a resource for information-processing tasks has inspired recent work on developing a resource theory based on non-Gaussianity [8][9][10]. In addition, it has been found that non-Gaussianity provides a certain degree of robustness in the presence of noise [11,12].…”

Section: Introductionmentioning

confidence: 99%

Enhanced continuous generation of non-Gaussianity through optomechanical modulation

et al. 2019

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We study the non-Gaussian character of quantum optomechanical systems evolving under the fully nonlinear optomechanical Hamiltonian. By using a measure of non-Gaussianity based on the relative entropy of an initially Gaussian state, we quantify the amount of non-Gaussianity induced by both a constant and time-dependent cubic light-matter coupling and study its general and asymptotic behaviour. We find analytical approximate expressions for the measure of non-Gaussianity and show that initial thermal phonon occupation of the mechanical element does not significantly impact the non-Gaussianity. More importantly, we also show that it is possible to continuously increase the amount of non-Gassuianity of the state by driving the light-matter coupling at the frequency of mechanical resonance, suggesting a viable mechanism for increasing the non-Gaussianity of optomechanical systems even in the presence of noise. Figure 1. An optomechanical system consisting of a moving end mirror. The operators â and â † denote the creation and annihilation operators for the light field, and b and b † denote the motional degree of freedom of the mirror. Other examples of optomechanical systems include levitated nanobeads and cold-atom ensembles. 7 We should note here that, since uncertainties in quantum Gaussian systems are fundamentally bounded by the Heisenberg uncertainty relation, which in principle does not hold for classical systems, Gaussian operations are in fact sufficient to run some protocols requiring genuine quantum features, such as continuous variable quantum key distribution.

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Section: Introductionmentioning

confidence: 99%

Enhanced continuous generation of non-Gaussianity through optomechanical modulation

et al. 2019

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“…A platform that is particularly promising for such applications is continuous-variable quantum optics, where large entangled graph states can be deterministically produced [5][6][7][8][9]. Even though this allows us to produce intricate quantum networks, the resulting Gaussian quantum states still have a positive Wigner function.Negativity of the Wigner function has been identified as a necessary ingredient for implementing processes that cannot be simulated efficiently with classical resources [10,11], and is therefore an essential resource [12,13] to achieve a quantum advantage. In networked quantum technologies it is, thus, crucial to generate and distribute Wigner-negativity in the nodes of a quantum network.…”

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confidence: 99%

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

Walschaers

Treps

2020

Phys. Rev. Lett.

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Negativity of the Wigner function is seen as a crucial resource for reaching a quantum computational advantage with continuous variable systems. However, these systems, while they allow for the deterministic generation of large entangle states, require an extra element such as photon subtraction to obtain such negativity. Photon subtraction is known to affect modes beyond the one where the photon is subtracted, an effect which is governed by the correlations of the state. In this manuscript, we build upon this effect to remotely prepare states with Wigner-negativity. More specifically, we show that photon subtraction can induce Wigner-negativity in a correlated mode if and only if that correlated mode can perform Einstein-Podolsky-Rosen steering in the mode of subtraction.Manipulating networks is at the heart of information processing and communication. Hence, the growing interest in a quantum internet [1, 2] is a logical step in the developments of quantum technologies. The key idea of such a quantum network, be it for communication or for distributed computation, is to connect a large number of nodes via quantum entanglement [3,4]. A platform that is particularly promising for such applications is continuous-variable quantum optics, where large entangled graph states can be deterministically produced [5][6][7][8][9]. Even though this allows us to produce intricate quantum networks, the resulting Gaussian quantum states still have a positive Wigner function.Negativity of the Wigner function has been identified as a necessary ingredient for implementing processes that cannot be simulated efficiently with classical resources [10,11], and is therefore an essential resource [12,13] to achieve a quantum advantage. In networked quantum technologies it is, thus, crucial to generate and distribute Wigner-negativity in the nodes of a quantum network. In this spirit we focus here on the remote generation of Wigner-negativity, such that operations in one node of a quantum network create negativity in the Wigner function of another node while upholding the entanglement in the quantum network.Photon subtraction [14-16] is a natural candidate for such operation. In previous work, we showed that the subtraction of a photon causes an interplay between correlations and non-Gaussian features [17]. In the specific case of graph states, it was shown that non-Gaussian properties, induced by photon subtraction, propagate through the system [18,19], however it is far from clear whether this mediated non-Gaussianity has quantum features (see also [20]). Hence, here we turn the question around, and ask what type of correlations are required to remotely generate negativity of the Wigner function through photon subtraction. We show that Einstein-Podolsky-Rosen (EPR) steering [21-25] is a necessary and sufficient condition.In its essence, EPR steering focusses on the the structure of conditional quantum probabilities: when Alice and Bob share a quantum state, Bob can perform measurements on his part of the state and Alice can condition her...

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“…1Compute the matrix Y whose existence is guaranteed by equation (35). 2Obtain g using equation (36). 3Determine σ (the ancilla state) from g using equation (8); this is possible by lemma 2.…”

Section: Lemma 7 [2]mentioning

confidence: 99%

“…In view of these limitations, it will not come as a surprise that a substantial effort has been put into developing a consistent resource theory of non-Gaussianity. Many non-Gaussianity measures have been proposed and studied in the past decade [31][32][33][34][35][36], that can be applied e.g. to bound the conversion rates between arbitrary states by means of Gaussian operations [35].…”

Section: Introductionmentioning

confidence: 99%

All phase-space linear bosonic channels are approximately Gaussian dilatable

2018

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We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation at the phase space level; and (b) Gaussian dilatable channels, that admit a Stinespring dilation involving a Gaussian unitary. Our main result is that the set (a) coincides with the closure of (b) with respect to the strong operator topology. We also present an example of a channel in (a) which is not in (b), implying that taking the closure is in general necessary. This provides a complete resolution to the conjecture posed in Sabapathy and Winter (2017 Phys. Rev. A 95 062309). Our proof technique is constructive, and yields an explicit procedure to approximate a given linear bosonic channel by means of Gaussian dilations. It turns out that all linear bosonic channels can be approximated by a Gaussian dilation using an ancilla with the same number of modes as the system. We also provide an alternative dilation where the unitary is fixed in the approximating procedure. Our results apply to a wide range of physically relevant channels, including all Gaussian channels such as amplifiers, attenuators, phase conjugators, and also non-Gaussian channels such as additive noise channels and photon-added Gaussian channels. The method also provides a clear demarcation of the role of Gaussian and non-Gaussian resources in the context of linear bosonic channels. Finally, we also obtain independent proofs of classical results such as the quantum Bochner theorem, and develop some tools to deal with convergence of sequences of quantum channels on continuous variable systems that may be of independent interest.

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Resource theory of quantum non-Gaussianity and Wigner negativity

Cited by 237 publications

References 121 publications

Enhanced continuous generation of non-Gaussianity through optomechanical modulation

Enhanced continuous generation of non-Gaussianity through optomechanical modulation

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

All phase-space linear bosonic channels are approximately Gaussian dilatable

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