Classical command of quantum systems

Reichardt, Ben W.; Unger, Falk; Vazirani, Umesh

doi:10.1038/nature12035

Cited by 353 publications

(472 citation statements)

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“…It guarantees that, for instance, pairs of photons can be treated as individual objects with individual properties and without any hidden correlations to other pairs. These, and many other results, addressed a number of subtleties and, finally, twenty years after its inception, the original entanglement-based key distribution protocol 7 has been shown to offer security even if the devices are not fully trusted and are exposed to noise 15,16,17,18,19,20 . This is assuming that quantum theory is all that there is, and that Eve is bound by the laws of quantum physics.…”

Section: Practicalitiesmentioning

confidence: 97%

“…Barring this, once the devices pass a certain statistical test they can be purchased without any knowledge of their internal working. This is a truly remarkable feat, also referred to as 'deviceindependent' cryptography 14,15,16,17,18,19,20 . Needless to say, proving security under such weak assumptions, with all the mathematical subtleties, is considerably more challenging than in the case of trusted devices, but the rapid progress in the past few years has been very encouraging, making device-independent cryptography one of the most active areas of quantum information science.…”

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confidence: 99%

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The ultimate physical limits of privacy

Ekert

Renner

2014

Nature

127

104

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Among those who make a living from the science of secrecy, worry and paranoia are just signs of professionalism. Can we protect our secrets against those who wield superior technological powers? Can we trust those who provide us with tools for protection? Can we even trust ourselves, our own freedom of choice? Recent developments in quantum cryptography show that some of these questions can be addressed and discussed in precise and operational terms, suggesting that privacy is indeed possible under surprisingly weak assumptions.Edgar Allan Poe, an American writer and an amateur cryptographer, once wrote "… it may be roundly asserted that human ingenuity cannot concoct a cipher which human ingenuity cannot resolve …" 1 . Is it true? Are we doomed to be deprived of our privacy, no matter how hard we try to retain it? If the history of secret communication is of any guidance here, the answer is a resounding 'yes'. There is hardly a shortage of examples illustrating how the most brilliant efforts of code-makers were matched by the ingenuity of code-breakers 2 . Even today, the best that modern cryptography can offer are security reductions, telling us, for example, that breaking RSA, one of the most widely used public key cryptographic systems, is at least as hard as factoring large integers 3 . But is factoring really hard? Not with quantum technology. Indeed, RSA, and many other public key cryptosystems, will become insecure once a quantum computer is built 4 . Admittedly, that day is probably decades away, but can anyone prove, or give any reliable assurance, that it is? Confidence in the slowness of technological progress is all that the security of our best ciphers now rests on.This said, the requirements for perfectly secure communication are well understood. When technical buzzwords are stripped away, all we need to construct a perfect cipher is shared private randomness, more precisely, a sequence of random bits known as a 'cryptographic key'. Any two parties who share the key, we call them Alice and Bob (not their real names, of course), can then use it to communicate secretly, using a simple encryption method known as the one-time pad 5 . The key is turned into a meaningful message by one party telling the other, in public, which bits of the key should be flipped. An eavesdropper, Eve, who has monitored the public communication and knows the general method of encryption but not the key will not be able to infer anything useful about the message. It is vital though that the key bits be truly random, never reused, and securely delivered to Alice and Bob, who may be miles apart. This is not easy, but it can be done, and one can only be amazed how well quantum physics lends itself to the task of key distribution.Quantum key distribution, proposed independently by Bennett and Brassard 6 and by Ekert 7 , derives its security either from the Heisenberg uncertainty principle (certain pairs of physical properties are complementary in the sense that knowing one property necessarily precludes knowledge about the othe...

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Section: Practicalitiesmentioning

confidence: 97%

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confidence: 99%

The ultimate physical limits of privacy

Ekert

Renner

2014

Nature

127

104

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“…Recently, Reichardt et al [146] proved a subtle robustness result for playing many instances of CHSH. Roughly, their result says: if a quantum protocol wins a fraction of nearly cos(π/8) 2 of a sequence of k given instances of the CHSH game, then most blocks of m = k Ω(1) instances have the property that they start "essentially" (again, up to local operations and small differences like in Theorem 16) from m EPR-pairs and run m independent instances of the standard protocol P * .…”

Section: Self-testing Protocolsmentioning

confidence: 99%

Untitled

Montanaro¹,

Wolf²

2016

Theory of Comput.

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“…It is well known that the probability over uniform inputs that they jointly win this game when they a priori share classical resources is 0.75, while if they share and appropriately measure a pair of maximally entangled qubits, they can jointly win the game with probability cos 2 π/8 > 0.75. The classical value 0.75 corresponds to the upper bound of a Bell inequality and the CHSH game provides an example of a Bell inequality violation, since there exist quantum strategies that violate this bound.Looking at Bell inequalities through the lens of games has been very useful in practice, including in cryptography [3,4] and quantum information [5], where, for example, quantum mechanics offers stronger than classical security guarantees in quantum key distribution or verification protocols. Recently, Brunner and Linden made the connection between Bell test scenarios and games with incomplete information more explicit and provided examples of such games where quantum mechanics offers an advantage [6].…”

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confidence: 99%

Nonlocality and Conflicting Interest Games

et al. 2015

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Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage. Nonlocality is one of the most important and elusive properties of quantum mechanics, where two spatially separated observers sharing a pair of entangled quantum bits can create correlations that cannot be explained by any local realistic theory. More precisely, Bell [1] showed that there exist scenarios where correlations between any local hidden variables can be shown to satisfy specific constraints (known as Bell inequalities), while these constraints can nevertheless be violated by correlations created by quantum systems.An equivalent way of describing Bell test scenarios is in the language of nonlocal games. The best-known example is the CHSH game [2]: Alice and Bob, who are spatially separated and cannot communicate, receive an input bit x and y respectively and must output bits a and b respectively, such that the outputs are different if both input bits are equal to 1, and the same otherwise. It is well known that the probability over uniform inputs that they jointly win this game when they a priori share classical resources is 0.75, while if they share and appropriately measure a pair of maximally entangled qubits, they can jointly win the game with probability cos 2 π/8 > 0.75. The classical value 0.75 corresponds to the upper bound of a Bell inequality and the CHSH game provides an example of a Bell inequality violation, since there exist quantum strategies that violate this bound.Looking at Bell inequalities through the lens of games has been very useful in practice, including in cryptography [3,4] and quantum information [5], where, for example, quantum mechanics offers stronger than classical security guarantees in quantum key distribution or verification protocols. Recently, Brunner and Linden made the connection between Bell test scenarios and games with incomplete information more explicit and provided examples of such games where quantum mechanics offers an advantage [6]. A game with incomplete information (or Bayesian game) is a game where the two parties receive some input unknown to the other party [7]. We remark that without more restrictions, quantum mechanics only offers advantages for incomplete information games, i.e., when the parties receive inputs or, in other word...

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Classical command of quantum systems

Cited by 353 publications

References 55 publications

The ultimate physical limits of privacy

The ultimate physical limits of privacy

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Nonlocality and Conflicting Interest Games

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