Operational Gaussian Schmidt-number witnesses

Shähandeh, Farid; Sperling, Jan; Vogel, W.

doi:10.1103/physreva.88.062323

Cited by 16 publications

(19 citation statements)

References 47 publications

(64 reference statements)

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“…However, it is not aimed at quantifying the amount of entanglement. For a quantification of Gaussian entanglement, one needs to employ entanglement measures (monotones); see, e.g., [43]. In the following, we will introduce the treatment of atmospheric fading channels.…”

Section: Gaussian Entanglement In Fading Channelsmentioning

confidence: 99%

Gaussian entanglement in the turbulent atmosphere

et al. 2016

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We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a non-trivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.

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Section: Gaussian Entanglement In Fading Channelsmentioning

confidence: 99%

Gaussian entanglement in the turbulent atmosphere

et al. 2016

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“…(B6) are submatrices of A (J) of Eq. (17) and that J = 0 so that Properties (i) and (ii) are fulfilled. From the decreasing order on the diagonal elements and Property (ii), we can show that the relation of Eq.…”

Section: Inequalities For the Spreading Shiftmentioning

confidence: 99%

“…A channel of Schmidt-class k is also referred to as k-partially entanglement breaking (k-PEB) since it represents an important class of completely positive (CP) maps called entanglement breaking in the case of k = 1 [7,8]. The notion of the Schmidt number tells us a precise meaning of the dimensionality in quantum object, and enables us to demonstrate multi-level coherences of quantum gates [9] as well as to verify higher order entanglement in practical conditions [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, it is natural to ask to what extent a given CV system is capable of simulating a higher dimensional quantum information process in practice. Notably, a verification scheme of higher dimensional entanglement of CV quantum states has been proposed [15,17]. However, it has little been studied how to verify higher dimensional gate coherences in CV quantum gates.…”

Section: Introductionmentioning

confidence: 99%

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Schmidt-number benchmarks for continuous-variable quantum devices

Namiki

2016

Phys. Rev. A

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We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most k-dimensional coherences for positive integers k. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is k. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two endpoints of k = 1 and k = ∞, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate can transmit a high dimensional coherence. The result is further extended to be applicable to general quantum operations or stochastic quantum channels. While the fidelity is often associated with heterodyne measurements in quantum optics, we can also obtain similar criteria based on quadrature deviations determined via homodyne measurements.

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“…While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.…”

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confidence: 99%

Measurement-Device-Independent Approach to Entanglement Measures

2017

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Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states. DOI: 10.1103/PhysRevLett.118.150505 Introduction.-Entanglement is a valuable resource for practical as well as fundamental applications of quantum theory, ranging from quantum computation and communication to metrology [1-3]. There are two major challenges in understanding entanglement that stimulates this research. First, it is extremely difficult to specify all the nonentangled bipartite or multipartite quantum states. In fact, the problem is known to be NP-hard [4,5]. Second, not surprisingly, the characterization of entangled states, i.e., the quantification of entanglement within quantum states, is an equally difficult task. The answer to the second challenge is practically very important because it tells us how well our protocols will perform using a given state [6][7][8][9].Focusing on the second challenge above, a first level of hardness is that the quantification of entanglement using almost any entanglement measure, e.g., entanglement of formation [10], negativity [11,12], or random robustness [13], requires estimating a large number of density matrix elements, a task which is difficult to perform on bipartite and multipartite quantum states. While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs). In any such game, two players (Alice and Bob) share a possibly entangled state. A referee (Charlie) starts by asking them

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Operational Gaussian Schmidt-number witnesses

Cited by 16 publications

References 47 publications

Gaussian entanglement in the turbulent atmosphere

Gaussian entanglement in the turbulent atmosphere

Schmidt-number benchmarks for continuous-variable quantum devices

Measurement-Device-Independent Approach to Entanglement Measures

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