Non-locality and Communication Complexity

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in Reviews of Modern Physic

Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes

It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors with fidelity exponentially close to 1, at the price of increasing the size of the registers (i.e., the coding alphabet). This demonstrates a sharp distinction between exact and approximate quantum error correction. The codes have the property that any $t$ components reveal no information about the message, and so they can also be viewed as error-tolerant secret sharing schemes. The construction has several interesting implications for cryptography and quantum information theory. First, it suggests that secret sharing is a better classical analogue to quantum error correction than is classical error correction. Second, it highlights an error in a purported proof that verifiable quantum secret sharing (VQSS) is impossible when the number of cheaters t is n/4. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure

Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures

In this paper, we address the problem of achieving efficient code-based digital signatures with small public keys. The solution we propose exploits sparse syndromes and randomly designed low-density generator matrix codes. Based on our evaluations, the proposed scheme is able to outperform existing solutions, permitting to achieve considerable security levels with very small public keys.Comment: 16 pages. The final publication is available at springerlink.co

Quantum Tokens for Digital Signatures

The fisherman caught a quantum fish. "Fisherman, please let me go", begged the fish, "and I will grant you three wishes". The fisherman agreed. The fish gave the fisherman a quantum computer, three quantum signing tokens and his classical public key. The fish explained: "to sign your three wishes, use the tokenized signature scheme on this quantum computer, then show your valid signature to the king, who owes me a favor". The fisherman used one of the signing tokens to sign the document "give me a castle!" and rushed to the palace. The king executed the classical verification algorithm using the fish's public key, and since it was valid, the king complied. The fisherman's wife wanted to sign ten wishes using their two remaining signing tokens. The fisherman did not want to cheat, and secretly sailed to meet the fish. "Fish, my wife wants to sign ten more wishes". But the fish was not worried: "I have learned quantum cryptography following the previous story (The Fisherman and His Wife by the brothers Grimm). The quantum tokens are consumed during the signing. Your polynomial wife cannot even sign four wishes using the three signing tokens I gave you". "How does it work?" wondered the fisherman. "Have you heard of quantum money? These are quantum states which can be easily verified but are hard to copy. This tokenized quantum signature scheme extends Aaronson and Christiano's quantum money scheme, which is why the signing tokens cannot be copied". "Does your scheme have additional fancy properties?" the fisherman asked. "Yes, the scheme has other security guarantees: revocability, testability and everlasting security. Furthermore, if you're at sea and your quantum phone has only classical reception, you can use this scheme to transfer the value of the quantum money to shore", said the fish, and swam away.Comment: Added illustration of the abstract to the ancillary file

Quantum Communication Cannot Simulate a Public Coin

We study the simultaneous message passing model of communication complexity. Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently showed that a large class of efficient classical public-coin protocols can be turned into efficient quantum protocols without public coin. This raises the question whether this can be done always, i.e. whether quantum communication can always replace a public coin in the SMP model. We answer this question in the negative, exhibiting a communication problem where classical communication with public coin is exponentially more efficient than quantum communication. Together with a separation in the other direction due to Bar-Yossef et al., this shows that the quantum SMP model is incomparable with the classical public-coin SMP model. In addition we give a characterization of the power of quantum fingerprinting by means of a connection to geometrical tools from machine learning, a quadratic improvement of Yao's simulation, and a nearly tight analysis of the Hamming distance problem from Yao's paper.Comment: 12 pages LaTe

Systematizing Genome Privacy Research: A Privacy-Enhancing Technologies Perspective

Rapid advances in human genomics are enabling researchers to gain a better understanding of the role of the genome in our health and well-being, stimulating hope for more effective and cost efficient healthcare. However, this also prompts a number of security and privacy concerns stemming from the distinctive characteristics of genomic data. To address them, a new research community has emerged and produced a large number of publications and initiatives. In this paper, we rely on a structured methodology to contextualize and provide a critical analysis of the current knowledge on privacy-enhancing technologies used for testing, storing, and sharing genomic data, using a representative sample of the work published in the past decade. We identify and discuss limitations, technical challenges, and issues faced by the community, focusing in particular on those that are inherently tied to the nature of the problem and are harder for the community alone to address. Finally, we report on the importance and difficulty of the identified challenges based on an online survey of genome data privacy expertsComment: To appear in the Proceedings on Privacy Enhancing Technologies (PoPETs), Vol. 2019, Issue

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the ground state and first fifteen excited singlet and triplet states within the coupled-cluster framework. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data was employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed $b^3\Sigma^+$, $a^3\Pi$, $A^1\Pi$, and $C^1\Pi$ states with subsequent efficient stabilization into the $v^{\prime\prime}=1$ vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from $v^{\prime\prime}=1$ to $v^{\prime\prime}=0$. Alternatively, photoassociation and stabilization to $v^{\prime\prime}=0$ can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds