Related papers: A direct product theorem for quantum communication…
We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we…
In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
A prominent application of quantum cryptography is the distribution of cryptographic keys that are provably secure. Recently, such security proofs were extended by Vazirani and Vidick (Physical Review Letters, 113, 140501, 2014) to the…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
We prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact…
We analyse two party non-local games whose predicate requires Alice and Bob to generate matching bits, and their three party extensions where a third player receives all inputs and is required to output a bit that matches that of the…
We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell…
Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorisation to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols like the one…
In device-independent quantum key distribution (DIQKD), an adversary prepares a device consisting of two components, distributed to Alice and Bob, who use the device to generate a secure key. The security of existing DIQKD schemes holds…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary…
A strong direct product theorem (SDPT) states that solving n instances of a problem requires Omega(n) times the resources for a single instance, even to achieve success probability exp(-Omega(n)). We prove that quantum communication…
We show optimal Direct Sum result for the one-way entanglement-assisted quantum communication complexity for any relation f subset of X x Y x Z. We show: Q^{1,pub}(f^m) = Omega(m Q^{1,pub}(f)), where Q^{1,pub}(f), represents the one-way…
We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for…
The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem…
We show that quantum query complexity satisfies a strong direct product theorem. This means that computing $k$ copies of a function with less than $k$ times the quantum queries needed to compute one copy of the function implies that the…
A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We…
Quantum secure direct communication (QSDC) can directly transmit secrete messages through quantum channel. Device-independent (DI) QSDC can guarantee the communication security relying only on the observation of the Bell inequality…
The laws of quantum mechanics allow unconditionally secure key distribution protocols. Nevertheless, security proofs of traditional quantum key distribution (QKD) protocols rely on a crucial assumption, the trustworthiness of the quantum…