Continuous-variable quantum key distribution protocols over noisy channels

A continuous-variable quantum key distribution protocol based on squeezed states and heterodyne detection is introduced and shown to attain higher secret key rates over a noisy line than any other one-way Gaussian protocol. This increased resistance to channel noise can be understood as resulting from purposely adding noise to the signal that is converted into the secret key. This notion of noise-enhanced tolerance to noise also provides a better physical insight into the poorly understood discrepancies between the previously defined families of Gaussian protocols.Comment: Minor modifications to match published manuscrip

Unconditional optimality of Gaussian attacks against continuous-variable QKD

A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all eavesdropping strategies, including collective and coherent attacks. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [Phys. Rev. Lett. 96, 080502 (2006)].Comment: 4 pages, 4 figure

Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions

We propose a scheme for the conditional generation of arbitrary finite superpositions of (squeezed) Fock states in a single mode of a traveling optical field. The suggested setup requires only a source of squeezed states, beam splitters, strong coherent beams, and photodetectors with single-photon sensitivity. The method does not require photodetectors with a high efficiency nor with a single-photon resolution.Comment: 9 pages, 9 figures, RevTeX

Percolation of secret correlations in a network

In this work, we explore the analogy between entanglement and secret classical correlations in the context of large networks, more precisely the question of percolation of secret correlations in a network. It is known that entanglement percolation in quantum networks can display a highly nontrivial behavior depending on the topology of the network and on the presence of entanglement between the nodes. Here we show that this behavior, thought to be of a genuine quantum nature, also occurs in a classical context.Comment: 6 pages, 3 figure

Limitations of optimization algorithms on noisy quantum devices

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians. Our approach is based on the combination of entropic inequalities that determine how fast the quantum computation state converges to the fixed point of the noise model, together with established classical methods of Gibbs state sampling. The approach is extremely versatile and allows for its application to a large variety of problems, noise models and quantum computing architectures. We use our result to provide estimates for a variety of problems and architectures that have been the focus of recent experiments, such as quantum annealers, variational quantum eigensolvers, and quantum approximate optimization. The bounds we obtain indicate that substantial quantum advantages are unlikely for classical optimization unless the current noise rates are decreased by orders of magnitude or the topology of the problem matches that of the device. This is the case even if the number of qubits increases substantially. We reach similar but less stringent conclusions for quantum Hamiltonian problems.Comment: 19 pages, 3 figure

A game of quantum advantage: linking verification and simulation

We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is supposed to demonstrate a quantum advantage. The other player, the skeptical Alice, is then allowed to propose mock distributions supposed to reproduce Bob's device's statistics. He then needs to provide witness functions to prove that Alice's proposed mock distributions cannot properly approximate his device. Within this framework, we establish three results. First, for random quantum circuits, Bob being able to efficiently distinguish his distribution from Alice's implies efficient approximate simulation of the distribution. Secondly, finding a polynomial time function to distinguish the output of random circuits from the uniform distribution can also spoof the heavy output generation problem in polynomial time. This pinpoints that exponential resources may be unavoidable for even the most basic verification tasks in the setting of random quantum circuits. Beyond this setting, by employing strong data processing inequalities, our framework allows us to analyse the effect of noise on classical simulability and verification of more general near-term quantum advantage proposals.Comment: 44 pages, to be published in Quantum. New version is substantially extended and contains new connections between previous results and the linear cross entrop

Strong converse for the classical capacity of optical quantum communication channels

We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier and free-space communication. The theorem holds under a particular photon-number occupation constraint, which we describe in detail in the paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links.Comment: 15 pages, final version accepted into IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1312.328

Quantum enhancement of randomness distribution

The capability of a given channel to transmit information is, a priori, distinct from its capability to distribute random correlations. Despite that, for classical channels, the capacity to distribute information and randomness turns out to be the same, even with the assistance of auxiliary communication. In this work we show that this is no longer true for quantum channels when feedback is allowed. We prove this by constructing a channel that is noisy for the transmission of information but behaves as a virtual noiseless channel for randomness distribution when assisted by feedback communication. Our result can be seen as a way of unlocking quantum randomness internal to the channel