Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations

Schneeloch, James; Broadbent, Curtis J.; Walborn, S. P.; Cavalcanti, Eric G.; Howell, John C.

doi:10.1103/physreva.87.062103

Cited by 291 publications

(283 citation statements)

References 41 publications

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“…In this case [23] it was found that the minimum error rate was 11%. Recently Branciard et al [22] showed that the key length in that case could be mapped to a different type of spatial steering inequality based on conditional entropies between Alice and Bob's qubits, in analogy to the entropic Bell and Leggett-Garg inequalities [26][27][28]. One can again map this entropic steering inequality into the temporal domain, which has the same error bound as the spatial one, producing a temporal entropic steering inequality:…”

Section: Chsh Inequalitymentioning

confidence: 99%

Temporal steering inequality

et al. 2014

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Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial applications in quantum information and communication science. Here, we highlight that there exists a natural temporal analogue of the steering inequality when considering measurements on a single object at different times. We give non-trivial operational meaning to violations of this temporal inequality by showing that it is connected to the security bound in the BB84 protocol and thus may have applications in quantum communication.

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Section: Chsh Inequalitymentioning

confidence: 99%

Temporal steering inequality

et al. 2014

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“…For example, it is crucial in the studies of quantum cryptography [1,2], entanglement detections [3,4], quantum steering [5,6], quantum nonlocalities [7,8], and so on. The original concept of the uncertainty relation was introduced by Heisenberg while demonstrating the impossibility of the simultaneous precise measurement of the position and momentum of an electron [9].…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of multi-observable uncertainty relations

Chen

Song

et al. 2017

Phys. Rev. A

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The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved lower bounds and were deemed capable of incorporating multiple observables. Here we report an experimental verification of seven uncertainty relations of this type with single-photon measurements. The results, while confirming these uncertainty relations, show as well the relative stringency of various uncertainty lower bounds.

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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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Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations

Cited by 291 publications

References 41 publications

Temporal steering inequality

Temporal steering inequality

Experimental investigation of multi-observable uncertainty relations

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

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