Computing conditional entropies for quantum correlations

Brown, Peter; Fawzi, Hamza; Fawzi, Omar

doi:10.1038/s41467-020-20018-1

Cited by 38 publications

(56 citation statements)

References 41 publications

(80 reference statements)

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“…It is likely that our entropy bound gives suboptimal results in the latter case. This is partly confirmed by a recent result for partially-entangled qubits in [14], where a threshold of about 84.3% is obtained for the global detection efficiency without using noise preprocessing, which is somewhat better than the thresholds of around 86.5% that we obtained for this case here.…”

Section: Discussionsupporting

confidence: 90%

“…A first motivation for considering these generalisations is purely theoretical. While we now understand how the security of a generic DIQKD protocol can be reduced to computing bounds on the conditional von Neumann entropy (or more precisely the derivation of what the authors of [7] call min-tradeoff functions), obtaining tight or reasonably good bounds beyond the already solved case of the CHSH expression, the simplest Bell expression, is challenging [11][12][13][14]. Our work shows how the von Neumann entropy can be computed for a new class of protocols and our approach, which partly relies on reducing the problem to the well-known BB84 protocol [15], might inspire further, more general, results.…”

Section: Introductionmentioning

confidence: 99%

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Device-independent quantum key distribution with asymmetric CHSH inequalities

Woodhead

Acín

Pironio

2021

Quantum

101

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The simplest device-independent quantum key distribution protocol is based on the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and allows two users, Alice and Bob, to generate a secret key if they observe sufficiently strong correlations. There is, however, a mismatch between the protocol, in which only one of Alice's measurements is used to generate the key, and the CHSH expression, which is symmetric with respect to Alice's two measurements. We therefore investigate the impact of using an extended family of Bell expressions where we give different weights to Alice's measurements. Using this family of asymmetric Bell expressions improves the robustness of the key distribution protocol for certain experimentally-relevant correlations. As an example, the tolerable error rate improves from 7.15% to about 7.42% for the depolarising channel. Adding random noise to Alice's key before the postprocessing pushes the threshold further to more than 8.34%. The main technical result of our work is a tight bound on the von Neumann entropy of one of Alice's measurement outcomes conditioned on a quantum eavesdropper for the family of asymmetric CHSH expressions we consider and allowing for an arbitrary amount of noise preprocessing.

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Section: Discussionsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Device-independent quantum key distribution with asymmetric CHSH inequalities

Woodhead

Acín

Pironio

2021

Quantum

101

View full text Add to dashboard Cite

show abstract

“…Al-though researchers have closed the detection loopholes in recent experiments with efficiency η ∼ 80% [12][13][14][15][16][17][18][19][20][21][22][23][24], a much higher efficiency, e.g., η > 90%, is normally required for the purpose of device-independent QKD [7][8][9][10][11]. Despite recent theory progress [26,27,[40][41][42][43][44][45][46], a practical implementation of device-independent QKD remains elusive.…”

mentioning

confidence: 99%

Photonic verification of device-independent quantum key distribution against collective attacks

Liu,

Zhang,

Zhen

et al. 2021

Preprint

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The security of quantum key distribution (QKD) [1,2] usually relies on that the users's devices are well characterized according to the security models made in the security proofs [3]. In contrast, device-independent QKD [4-11] -an entanglement-based protocol [2] -permits the security even without any knowledge of the underlying devices. Despite its beauty in theory, device-independent QKD is elusive to realize with current technology. This is because a faithful realization requires a high-quality violation of Bell inequality without the fair-sampling assumption [12,13]. Particularly, in a photonic realization, a rather high detection efficiency is needed where the threshold values depend on the security proofs [7][8][9][10][11]; this efficiency is far beyond the current reach [12][13][14][15][16][17][18][19][20][21][22][23][24]. Here, both theoretical and experimental innovations yield the realization of device-independent QKD based on a photonic setup. On the theory side, to relax the threshold efficiency for practical deviceindependent QKD, we exploit the random post-selection [25] combined with adding noise [26] for preprocessing, and compute the entropy with complete nonlocal correlations [27]. On the experiment side, we develop a high-quality polarization-entangled photonic source and achieve state-of-theart (heralded) detection efficiency of 87.49%, which outperforms previous experiments [12][13][14][15][16][17][18][19][20][21][22][23][24] and satisfies the threshold efficiency for the first time. Together, we demonstrate device-independent QKD at a secret key rate of 466 bits/s over 20 m standard fiber in the asymptotic limit against collective attacks. Besides, we show the feasibility of generating secret keys at a fiber length of 220 meters. Importantly, our photonic implementation can generate entangled photons at a high rate and in the telecom wavelength, which is desirable for high-speed key generation over long distances. The results not only prove the feasibility of device-independent QKD with realistic devices, but also push the security of communication to an unprecedented level.

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“…Nevertheless, for the purpose of device-independent QKD, a much higher efficiency, e.g., η > 90%, is required with the conventional security proofs [17,[21][22][23][24], which is far beyond the current technologies. To lower the threshold efficiency, recent works have proposed different approaches, such as efficient post-processing [31], two-way classical communication [32], noisy preprocessing [33], generalized Bell inequalities [34][35][36], complete statistics via von Neumann entropy [37,38] and multiple key-generation basis [39].…”

mentioning

confidence: 99%

Device-independent quantum key distribution with random postselection

Xu,

Zhang,

Zhang

et al. 2021

Preprint

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Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain little correlations but contribute high errors. Here we propose the device-independent QKD protocol with random post selection, where the secret keys are extracted only from the post-selected subset of outcomes. This could not open the detection loophole as long as the entropy of the post-selected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This post selection has the advantage to significantly reduce the error events, thus relaxing the threshold of required detection efficiency. In the model of collective attacks, our protocol can tolerate detector efficiency as low as 68.5%, which goes beyond standard security proofs. The results make a concrete step for the implementation of device-independent QKD in practice.

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Computing conditional entropies for quantum correlations

Cited by 38 publications

References 41 publications

Device-independent quantum key distribution with asymmetric CHSH inequalities

Device-independent quantum key distribution with asymmetric CHSH inequalities

Photonic verification of device-independent quantum key distribution against collective attacks

Device-independent quantum key distribution with random postselection

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