Exponential separation of quantum and classical one-way communication complexity

Bar-Yossef, Ziv; Jayram, T. S.; Kerenidis, Iordanis

doi:10.1145/1007352.1007379

Cited by 101 publications

(138 citation statements)

References 23 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…Another example is the CHSH game, where we can assume that both Alice and Bob win 1 point if the parity of their outputs is equal to the logical AND of their inputs, and they lose 1 point otherwise (see Example 1 in [6]). In fact, other known nonlocal games, including the GHZ-Mermin game [10], the Magic Square Game [11,12], the Hidden Matching game [13,14], Brunner and Linden's three games [6], are all examples of common interest games [25].…”

mentioning

confidence: 99%

Nonlocality and Conflicting Interest Games

et al. 2015

Self Cite

View full text Add to dashboard Cite

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...

show abstract

mentioning

confidence: 99%

Nonlocality and Conflicting Interest Games

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has been shown that in the bounded-error model, any classical protocol requires Ω( √ n) bits of communication [11]. It was also shown in Ref.…”

Section: Quantum Communication Complexitymentioning

confidence: 76%

“…Likewise, quantum communication complexity studies the case where the parties are allowed to employ quantum resources such as quantum channels and shared entanglement [2,26]. Remarkably, it has been proven that there exist various problems for which the use of quantum resources offer exponential savings in communication compared to their classical counterparts [8][9][10][11]27]. In this section, our goal is to employ the mapping to construct protocols that can be implemented using only coherent states and linear optics.…”

Section: Quantum Communication Complexitymentioning

confidence: 99%

“…This question has been a driving force of numerous research endeavours over the last few decades and remarkable progress has been made in our understanding of the advantages that quantum mechanics can provide, as well is in developing the experimental platforms that will allow them to be realized in practice [1][2][3][4]. An example is the field of quantum communication [5], where quantum systems can be used, for instance, to distribute secret keys [6,7] or reduce the amount of communication required for joint computations [8][9][10][11].In terms of experimental implementations, only quantum key distribution (QKD) has been routinely demonstrated and deployed over increasingly complex networks and large distances [12,13]. This is possible largely due to the fact that, fundamentally, QKD can be carried out with sequences of independent signals and measurements [4].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quantum communication with coherent states and linear optics

Arrazola

Lütkenhaus

2014

Phys. Rev. A

View full text Add to dashboard Cite

We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming protocols in quantum communication into a form in which they can be implemented with current technology. We explore the similarity between properties of the original qubit protocols and the coherent-state protocols obtained from the mapping and make use of the mapping to construct new protocols in the context of quantum communication complexity and quantum digital signatures. Our results have the potential of bringing a wide class of quantum communication protocols closer to their experimental demonstration.What information-processing tasks are unachievable in a classical world but become possible when exploiting the intrinsic quantum mechanical properties of physical systems? This question has been a driving force of numerous research endeavours over the last few decades and remarkable progress has been made in our understanding of the advantages that quantum mechanics can provide, as well is in developing the experimental platforms that will allow them to be realized in practice [1][2][3][4]. An example is the field of quantum communication [5], where quantum systems can be used, for instance, to distribute secret keys [6,7] or reduce the amount of communication required for joint computations [8][9][10][11].In terms of experimental implementations, only quantum key distribution (QKD) has been routinely demonstrated and deployed over increasingly complex networks and large distances [12,13]. This is possible largely due to the fact that, fundamentally, QKD can be carried out with sequences of independent signals and measurements [4]. Other tasks typically require sophisticated quantum states to be prepared and transmitted as well as performing complex operations on them. Overall, there is a large set of quantum communication protocols whose potential advantages currently escape the grasp of available technology, with only a few proof-of-principle implementations having been reported [14][15][16].Confronted with these challenges we face two alternatives: We can either strive to improve current technology or we can flip the issue around and ask: Can protocols in quantum communication be adapted to a form that makes them ready to be deployed with available techniques? To adopt the latter strategy is to push for a theoretical reformulation that converts previously intractable protocols into a form that, while conserving their relevant features, eliminates the obstacles affecting their implementation. This is precisely the road that has already been successfully followed for QKD.In this work, we describe an abstract mapping that converts quantum communication protocols that use pure states of multiple qubits, ...

show abstract

“…The scheme was based on hidden matching quantum retrieval games (QRGs), first introduced in Ref. [27]. Nevertheless, the scheme could not be considered practical, as the security analysis did not include the effects of noise.…”

Section: Introductionmentioning

confidence: 99%

Quantum money with nearly optimal error tolerance

Amiri

Arrazola

2017

Phys. Rev. A

View full text Add to dashboard Cite

We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which we conjecture reaches 25% asymptotically as the dimension of the underlying hidden matching states is increased. Furthermore, we prove that 25% is the maximum tolerable noise for a wide class of quantum money schemes with classical verification, meaning our schemes are almost optimally noise tolerant. We use methods in semidefinite programming to prove security in a substantially different manner to previous proposals, leading to two main advantages: first, coin verification involves only a constant number of states (with respect to coin size), thereby allowing for smaller coins; second, the re-usability of coins within our scheme grows linearly with the size of the coin, which is known to be optimal. Lastly, we suggest methods by which the coins in our protocol could be implemented using weak coherent states and verified using existing experimental techniques, even in the presence of detector inefficiencies.

show abstract

Exponential separation of quantum and classical one-way communication complexity

Cited by 101 publications

References 23 publications

Nonlocality and Conflicting Interest Games

Nonlocality and Conflicting Interest Games

Quantum communication with coherent states and linear optics

Quantum money with nearly optimal error tolerance

Contact Info

Product

Resources

About