Measurement-device-independent quantification of entanglement for given Hilbert space dimension

Goh, Koon Tong; Bancal, Jean-Daniel; Scarani, Valerio

doi:10.1088/1367-2630/18/4/045022

Cited by 36 publications

(46 citation statements)

References 24 publications

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“…In [23] it was first shown that the Shor-Preskill rate still holds if no correlations are observed in the mismatched bases cases assuming that Alice performs unknown projective qubit measurements. A similar result was recovered numerically in [24] for general qubit POVMs on Alice's side, assuming that Bob also performs qubit measurements. The prepare-and-measure version of BB84 was also studied numerically in [25] at a similar level of device independence, where Alice's source prepares unknown pure qubit states and Bob performs unknown projective qubit measurements.…”

Section: Bb84 and Device Independencesupporting

confidence: 69%

Semi device independence of the BB84 protocol

Woodhead

2016

New J. Phys.

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The BB84 quantum key distribution protocol is semi device independent in the sense that it can be shown to be secure if just one of the users' devices is restricted to a qubit Hilbert space. Here, we derive an analytic lower bound on the asymptotic secret key rate for the entanglement-based version of BB84 assuming only that one of the users performs unknown qubit POVMs. The result holds against the class of collective attacks and reduces to the well known Shor-Preskill key rate for correlations corresponding to the ideal BB84 correlations mixed with any amount of random noise.

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Section: Bb84 and Device Independencesupporting

confidence: 69%

Semi device independence of the BB84 protocol

Woodhead

2016

New J. Phys.

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“…Among the results presented in this issue, [35] study a 'semi-device-independent' (SDI) model in which one of the devices is trusted; in this scenario they provide improved quantitative bounds for the problem of selftesting an EPR pair, with an analysis based on the phenomenon of EPR steering. [12] considers another SDI model, one in which only the dimension of the system is known but not the measurements, and provides tools to quantify entanglement and security proofs for QKD. [40] studies the security of BB84 under the even weaker assumption that the dimension of only one of the systems is constrained to be a qubit.…”

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confidence: 99%

Focus on device independent quantum information

2016

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The field of quantum information is born out of a sequence of surprising discoveries in the 1980s, all building on the same deep insight: the counter-intuitive quantum properties of particles such as photons or electrons can be put to task in order to accomplish certain computational, cryptographic, and information-theoretic tasks impossible to realize by purely classical means. A famous example is the cryptographic problem of key distribution, for which Bennett and Brassard devised the first quantum protocol in 1984 [6] and whose security relies on the no-cloning principle of quantum mechanics. Another example is the computational problem of factoring large numbers, for which Shor devised the first efficient quantum algorithm in 1994 [32] by exploiting the possibility for quantum systems to evolve in superpositions of exponentially many different states.In this early history, and until very recently, the violation of Bell inequalities was simply seen as yet another feature distinguishing the quantum processing of information from a classical one. It provided one of the initial motivations for developing a better understanding of entangled states; it was recognized as a key factor responsible for the quantum advantage in communication complexity protocols; it was frequently used in experiments to demonstrate oneʼs ability to generate and manipulate entanglement. It also played an important conceptual role, as it established that the predictions of quantum theory, including its claimed information processing advantages, could not be naively reproduced by a classical theory. But overall the manifestation of quantum non-locality was just another way to evidence the weirdness of quantum theory, on par with the nocloning principle or the uncertainty of quantum measurements in having little consequence for practical applications.In very recent years, however, the violation of Bell inequalities has acquired a special status that is starting to revolutionize our understanding of the information-theoretic possibilities of quantum information. Indeed, not only are the properties of quantum states and measurements leading to the violation of Bell inequalities unique in the sense of having no classical explanation, but they also often uniquely single out the quantum system itself. More precisely, given a black-box device that is verifiably violating a Bell inequality, quantum theory allows for a virtually unique way in which this can be accomplished. Furthermore, for the many tasks for which quantum information provides an advantage, there often turns out to be a protocol whose advantage essentially amounts to the sufficiently large violation of a certain Bell inequality.Taken together, these two phenomena lead to the following observation: it is possible to devise quantum information protocols whose correctness can be certified even when they are run with untrusted quantum devices, on which no a priori assumptions are made. Hence the name 'device-independence' (DI) to refer to such protocols. The implications of this are pr...

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“…In Example 2 we have considered a 2 ⊗ 2 separable mixed state (41) having both nonzero Alice to Bob and non-zero Bob to Alice discord. We have shown that the correlation (42) produced by performing some particular local noncommuting measurements on this state can be simulated with LHV-LHS model with random variable having minimum dimension 3.…”

Section: Quantumness As Captured By Super-unsteerabilitymentioning

confidence: 99%

“…This implies that the correlation (42) cannot be simulated by classical-quantum state with dimension 2 ⊗ 2. Hence, the super-unsteerable correlation (42) certifies quantumness of certain 2 ⊗ 2 dimensional resources producing it and provides operational characterization of quantumness of the state (41).…”

Section: Quantumness As Captured By Super-unsteerabilitymentioning

confidence: 99%

Operational characterization of quantumness of unsteerable bipartite states

et al. 2018

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Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A 95, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as super-correlation, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be super-correlated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of super-unsteerability, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories. * debarshidas@jcbose.ac.in †

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Measurement-device-independent quantification of entanglement for given Hilbert space dimension

Cited by 36 publications

References 24 publications

Semi device independence of the BB84 protocol

Semi device independence of the BB84 protocol

Focus on device independent quantum information

Operational characterization of quantumness of unsteerable bipartite states

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