Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

Walborn, S. P.; Salles, A.; Gomes, Rafael M.; Toscano, Fabricio; Ribeiro, P. H. Souto

doi:10.1103/physrevlett.106.130402

Phys. Rev. Lett.

2011

DOI: 10.1103/physrevlett.106.130402

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Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

S. P. Walborn

A. Salles

Rafael M. Gomes

et al.

Abstract: Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observ… Show more

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Cited by 280 publications

(296 citation statements)

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“…We note here that sumfrequency generation does not have the same experimental history as SHG in quantum optics, mainly having been used for spectroscopy, and has quite different stability properties. Recent works have developed entropic functions for the detection of steering, which show some promise for further investigations of possible asymmetry [20,21]. In this Rapid Communication we will show that the relatively simple system 051802-1 1050-2947/2013/88(5)/051802(4)…”

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Asymmetric Gaussian harmonic steering in second-harmonic generation

Olsen

2013

Phys. Rev. A

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Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering. [3,4], is one of the central features which differentiates quantum mechanics from classical physics. It has previously been shown that SHG can be used to produce entangled fields at the two frequencies [5,6], later called "harmonic entanglement" by Grosse et al. [7].EPR expressed the original paradox in terms of position and momentum measurements. The essential step in their argument was to introduce correlated (entangled) states of at least two particles which persisted when the particles become spatially separated. According to EPR, depending on which property of one group of particles that was measured, a prediction with some certainty of the values of physical quantities of the other group of particles could be made. If these properties were represented by noncommuting operators (such as position and momentum), the Heisenberg uncertainty principle could seemingly be violated. The EPR conclusion was therefore that the description of physical reality given by quantum mechanics is not complete.In this Rapid Communication we use the continuousvariable (CV) characterization of EPR first put on a mathematical footing by Reid [8], using quadrature amplitudes, which have the same mathematical properti...

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Asymmetric Gaussian harmonic steering in second-harmonic generation

Olsen

2013

Phys. Rev. A

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“…Walborn et al [10] have improved the situation by introducing an entropic steering inequality. According to this criterion, states admitting LHS models satisfy…”

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Fine-grained Einstein-Podolsky-Rosen–steering inequalities

2014

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We derive a new steering inequality based on a fine-grained uncertainty relation to capture EPRsteering for bipartite systems. Our steering inequality improves over previously known ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangle states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the CHSH inequality. Finally, we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device independent quantum key distribution protocol secure against individual attacks. To show this result, we first derive a monogamy relation for our steering inequality. The development of quantum information led to distinguish three forms of non-local correlations in quantum physics [1][2][3][4][5][6]. These are entanglement, steering and Bell non-local correlations. Einstein, Podolsky and Rosen (EPR) introduced entangled quantum states in an attempt to show the incompleteness of quantum physics known as the EPR paradox [1]. The same year, Schrödinger re-expressed the EPR paradox as the possibility of steering (more generally, known as EPRsteering), i.e., when Alice and Bob share an entangled state, Alice can affect Bob's state throught her own measurement. More precisely, a state exhibits EPR-steering if it cannot be modeled as Bob holding an unknown yet definite state, a description known as a local hidden state (LHS) model [4]. Bell-type inequalities can be used to rule out local hidden variable (LHV) models. Similarly, steering inequalities are used to rule out the existence of LHS model and thus, demonstrate steerability.According to Wiseman, Jones and Doherty, the three forms of non-local correlations are also tightly related to the experimental settings required to test them [4]. To test entanglement, both parties need to trust that they perform quantum operations and also trust their measurement devices. In the case of EPR-steering, only one party assumes that he applies a quantum measurement and that his device is not controlled by a third party. Finally, Bell non-locality can be be tested without assuming quantum theory and trusting measurement devices. This leads to a hierarchy in which EPR-steering lies between Bell non-locality and entanglement.Experimental demonstration of Bell's non-locality has been achieved by several experiments [7]. To test EPRsteering, Reid proposed a testable formulation for continuous variable systems based on the position-momentum uncertainty relation [5]. Denote (X, P x ) and (Y, P y ) the position and corresponding momentum of two correlated modes. According to the Reid criterion, one needs to infer the uncertainty (measured by the standard deviation) of the quadrature amplitude X θk = cos[θk]X + sin[θk]P x for k ∈ {1, 2} from the measurement outcome of the correlated amplitude Y φk = cos[φ...

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“…Later, Walborn et al [4] developed a steering inequality using an entropic [14] formulation of the uncertainty principle for CV position and momentum [15]. For all states whose spatial correlations are insufficient to demonstrate the EPR paradox, the inequality,…”

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“…Violating EPR steering for continuous variables (CV) is understandably challenging because CV systems are infinitedimensional. As interest in EPR steering increases, including interest regarding its fundamental aspects [3][4][5][6][7][8][9], as well as its use in quantum information applications such as secure quantum key distribution [10], witnesses of CV EPR steering become increasingly important.…”

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

et al. 2013

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Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

Cited by 280 publications

References 19 publications

Asymmetric Gaussian harmonic steering in second-harmonic generation

Asymmetric Gaussian harmonic steering in second-harmonic generation

Fine-grained Einstein-Podolsky-Rosen–steering inequalities

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

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