arXiv subjects

M. Ben-Or

Publications and source records attributed to M. Ben-Or.

4 recordsLinked to original sources

arXiv2008

Simple and secure quantum key distribution with biphotons

The best qubit one-way quantum key distribution (QKD) protocol can tolerate up to 14.1% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three level quantum system - a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. This is the first time, to the best of our knowledge, that the security of qutrit QKD protocols is rigorously analyzed against general attacks.

quant-ph↗

arXiv2007

Quantum Search in an Ordered List via Adaptive Learning

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a noisy answer is returned We present a (classic) algorithm which optimally solves both variants together, up to an additive term of O(\log \log(n)), and prove matching information theoretic lower bounds. We use the algorithm to improve the results of Farhi et al \cite{FGGS99} presenting a quantum (error free) search algorithm in an ordered list of expected complexity less than (\log_2n) / 3.

quant-ph↗

arXiv2004

The Universal Composable Security of Quantum Key Distribution

The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first derive a composable security definition for QKD. We then prove that the usual security definition of QKD still implies the composable security definition. Thus, a key produced in any QKD protocol that is unconditionally secure in the usual definition can indeed be safely used, a property of QKD that is hitherto unproven. We propose two other useful sufficient conditions for composability. As a simple application of our result, we show that keys generated by repeated runs of QKD degrade slowly.

quant-ph↗

arXiv1996

Limitations of Noisy Reversible Computation

Noisy computation and reversible computation have been studied separately, and it is known that they are as powerful as unrestricted computation. We study the case where both noise and reversibility are combined and show that the combined model is weaker than unrestricted computation. In our noisy reversible circuits, each wire is flipped with probability p each time step, and all the inputs to the circuit are present in time 0. We prove that any noisy reversible circuit must have size exponential in its depth in order to compute a function with high probability. This is tight as we show that any circuit can be converted into a noise-resistant reversible one with a blow up in size which is exponential in the depth. This establishes that noisy reversible computation has the power of the complexity class NC^1. We extend this to quantum circuits(QC). We prove that any noisy QC which is not worthless, and for which all inputs are present at time 0, must have size exponential in its depth. (This high-lights the fact that fault tolerant QC must use a constant supply of inputs all the time.) For the lower bound, we show that quasi-polynomial noisy QC are at least powerful as logarithmic depth QC, (or QNC^1). Making these bounds tight is left open in the quantum case.

quant-ph↗