Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

Schneeloch, James; Dixon, Paul; Howland, Gregory A.; Broadbent, Curtis J.; Howell, John C.

doi:10.1103/physrevlett.110.130407

Cited by 87 publications

(95 citation statements)

References 19 publications

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“…Even though, the topic of entropic uncertainty relations (EURs) has a long history (for a detailed review see [4,5]), one can observe a recent increase of interest within the quantum information community leading to several improvements [6][7][8][9][10][11][12][13][14][15][16][17] or even a deep asymptotic analysis of different bounds [18]. This is quite understandable, because the entropic uncertainty relations have various applications, for example in entanglement detection [19][20][21][22][23], security of quantum protocols [24,25], quantum memory [26,27] or as an ingredient of Einstein-Podolsky-Rosen steering criteria [28,29]. Moreover, the recent discussion [30] about the original Heisenberg idea of uncertainty, led to the entropic counterparts of the noise-disturbance uncertainty relation [31,32] (also obtained with quantum memory [33]).…”

Section: Introductionmentioning

confidence: 99%

Majorization approach to entropic uncertainty relations for coarse-grained observables

Rudnicki

2015

Phys. Rev. A

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We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The obtained entropic inequalities involve two Rényi entropies of the same order, and thus go beyond the standard scenario with conjugated parameters. In a special case describing the sum of two Shannon entropies the majorization-based bounds significantly outperform the currently known results in the regime of larger coarse graining, and might thus be useful for entanglement detection in continuous variables.

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Section: Introductionmentioning

confidence: 99%

Majorization approach to entropic uncertainty relations for coarse-grained observables

Rudnicki

2015

Phys. Rev. A

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“…For example, by exploiting steering it is possible to obtain key rates unachievable in a full device-independent approach [11], but still assuming less about the devices than in a standard QKD approach [12]. For these reasons, steering has attracted a lot of interest in recent times, both theoretically and experimentally [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], mostly directed to the verification of steering. Nonetheless, an answer to the question "What is steering useful for?"…”

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confidence: 99%

Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering

2015

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Steering is the entanglement-based quantum effect that embodies the "spooky action at a distance" disliked by Einstein and scrutinized by Einstein, Podolsky, and Rosen. Here we provide a necessary and sufficient characterization of steering, based on a quantum information processing task: the discrimination of branches in a quantum evolution, which we dub subchannel discrimination. We prove that, for any bipartite steerable state, there are instances of the quantum subchannel discrimination problem for which this state allows a correct discrimination with strictly higher probability than in absence of entanglement, even when measurements are restricted to local measurements aided by one-way communication. On the other hand, unsteerable states are useless in such conditions, even when entangled. We also prove that the above steering advantage can be exactly quantified in terms of the steering robustness, which is a natural measure of the steerability exhibited by the state. Not all entangled states are steerable, and not all steerable states exhibit nonlocality [4,5], but states that exhibit steering allow for the verification of their entanglement in a semi-device independent way: there is no need to trust the devices used by the steering party, and the ability to determine the conditional states of the steered party is sufficient [4,5,9]. In general, besides its foundational interest, steering is interesting in practice in bipartite tasks, like quantum key distribution (QKD) [10], where it is convenient and/or appropriate to trust the devices of one of two parties, but not necessarily of the other party. For example, by exploiting steering it is possible to obtain key rates unachievable in a full device-independent approach [11], but still assuming less about the devices than in a standard QKD approach [12]. For these reasons, steering has attracted a lot of interest in recent times, both theoretically and experimentally [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], mostly directed to the verification of steering. Nonetheless, an answer to the question "What is steering useful for?" that applies to states that exhibit steering can arguably be considered limited [9,12]. Furthermore, the quantification of steering has just started to be addressed [24].In this Letter we fully characterize and quantify steering in an operational way that nicely matches the asymmetric features of steering, and that breaks new ground in the investigation of the usefulness of steering. We prove that every steerable state is a resource in a quantum information task that we dub subchannel discrimination, in a practically relevant scenario where measurements can only be performed locally.Subchannel discrimination is the identification of which branch of a quantum evolution a quantum system undergoes (see Fig. 1). It is well known that entanglement between a probe and an ancilla can help in discriminating different channels [31][32][33][34][35][36][37][38][39][40][41]. In [42] it was proven that actually every ...

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“…where H(X s |X i ) the conditional entropy of the signal position on the idler position, while H(K s |K i ) is similarly defined for momentum [5]. The terms ∆x and ∆k are the pixel sizes in the image and Fourier planes, respectively.…”

Section: Resultsmentioning

confidence: 99%

Using Double Compressive Sensing in Simultaneous Imaging of Spatial Entanglement

et al. 2015

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Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

Cited by 87 publications

References 19 publications

Majorization approach to entropic uncertainty relations for coarse-grained observables

Majorization approach to entropic uncertainty relations for coarse-grained observables

Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering

Using Double Compressive Sensing in Simultaneous Imaging of Spatial Entanglement

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