Insider-proof encryption with applications for quantum key distribution

It has been pointed out that current protocols for device independent quantum key distribution can leak key to the adversary when devices are used repeatedly and that this issue has not been addressed. We introduce the notion of an insider-proof channel. This allows us to propose a means by which devices with memories could be reused from one run of a device independent quantum key distribution protocol to the next while bounding the leakage to Eve, under the assumption that one run of the protocol could be completed securely using devices with memories.Comment: 20 pages, version 2: new presentation introducing the insider-proof channel as a cryptographic elemen

More Randomness from the Same Data

Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment [Christensen et al., Phys. Rev. Lett. 111, 130406 (2013)], we show that about twice as much randomness as previously reported can be potentially extracted from this setup.Comment: 6 pages + appendices, 4 figures, v3: version close to the published one. See also the related work arXiv:1309.393

Reference Frames and Algorithms for Quantum Information Processing

The main results of this thesis fall in to two areas, firstly quantum reference frames as a resource for quantum computations and secondly quantum algorithms. The results relating to quantum references consider their scaling with a requirements to perform measurements, operations and computations with a certain fidelity. For the case of a directional frame, the central question considered is of how many operations or measurements can be performed with it before its fidelity falls below some threshold. This is found to scale as the square of the size of the reference frame under for a range of physically interesting cases. To prove that result a new general form for any rotationally invariant map. This could have many applications is comparing and classifying rotationally invariant behaviour of quantum systems. Phase references are also considered for the case of performing quantum computations under an energy conservation law. The restriction that the expected energy be conserved for large quantum computations is shown to be manageable in many different potential architectures. In the case of completing computations is an energy conserving subspace, the requirements for ancillas are sublinear in the number of qubits, and even in a circuit model implementation, the errors due to phase reference imperfections are shown to not limit the apparent algorithmic improvements of quantum computing over classical computing. A quantum walk for the novel concept of two entangled walkers is proposed and analyzed. A modest improvement is found in the scaling of the expected separation of the walkers over the separable case. It illustrates the potential for making use of particle statistic behaviour in algorithms. Lastly, the relation between discrete and continuous time models of quantum computing is explored through the analysis of a new algorithm for simulating the Hamiltonian behaviour of a black box unitary operation. The scaling of the number of calls to the unitary required to obtain a simulation correct to within a parameter ϵ is found, as is a case where the efficiency of the algorithm is superior to directly applying the unitary repeatedly. Applications of the algorithm are considered

Efficient excitation of a two level atom by a single photon in a propagating mode

State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized \textit{propagating} pulse in free space and study the probability $P_e(t)$ of finding the atom in the excited state at any time $t$. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\Lambda\in[0,8\pi/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then $P_e(t)$ can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single photon Fock state and coherent states and for various temporal shapes of the pulses.Comment: 6 pages, 5 figures, 2 table

Security Proof for Quantum Key Distribution Using Qudit Systems

We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with $d$. The finite-key corrections are found to be almost insensitive to $d\lesssim 20$.Comment: 5 pages, 1 figure, version 3 corrects equations (9) and (11), and slightly modifies the figure to reflect the change to equation (11

Tomographic Quantum Cryptography Protocols are Reference Frame Independent

We consider the class of reference frame independent protocols in d dimensions for quantum key distribution, in which Alice and Bob have one natural basis that is aligned and the rest of their frames are unaligned. We relate existing approaches to tomographically complete protocols. We comment on two different approaches to finite key bounds in this setting, one direct and one using the entropic uncertainty relation and suggest that the existing finite key bounds can still be improved.Comment: Published version. 8 pages, 1 figur

Finite-key security against coherent attacks in quantum key distribution

The work by Christandl, K\"onig and Renner [Phys. Rev. Lett. 102, 020504 (2009)] provides in particular the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then we apply it to the study of a recently proposed protocol [Laing et al., Phys. Rev. A 82, 012304 (2010)]. This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because if one waits too long time, the average correlations are smeared out and no security can be inferred. Therefore, finite-key analysis is necessary to find the maximal achievable secret key rate and the corresponding optimal number of signals.Comment: 9 pages, 4 figure

Quantum Bell inequalities from macroscopic locality

10.1103/PhysRevA.83.022105Physical Review A - Atomic, Molecular, and Optical Physics832-PLRA