44 research outputs found
ADVANCES IN QUANTUM KEY DISTRIBUTION AND QUANTUM RANDOMNESS GENERATION
Ph.DDOCTOR OF PHILOSOPH
Randomness in post-selected events
Bell inequality violations can be used to certify private randomness for use
in cryptographic applications. In photonic Bell experiments, a large amount of
the data that is generated comes from no-detection events and presumably
contains little randomness. This raises the question as to whether randomness
can be extracted only from the smaller post-selected subset corresponding to
proper detection events, instead of from the entire set of data. This could in
principle be feasible without opening an analogue of the detection loophole as
long as the min-entropy of the post-selected data is evaluated by taking all
the information into account, including no-detection events. The possibility of
extracting randomness from a short string has a practical advantage, because it
reduces the computational time of the extraction.
Here, we investigate the above idea in a simple scenario, where the devices
and the adversary behave according to i.i.d. strategies. We show that indeed
almost all the randomness is present in the pair of outcomes for which at least
one detection happened. We further show that in some cases applying a
pre-processing on the data can capture features that an analysis based on
global frequencies only misses, thus resulting in the certification of more
randomness. We then briefly consider non-i.i.d strategies and provide an
explicit example of such a strategy that is more powerful than any i.i.d. one
even in the asymptotic limit of infinitely many measurement rounds, something
that was not reported before in the context of Bell inequalities.Comment: similar to published version, new section (III) on photonic
experiment
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
Practical and reliable error bars for quantum process tomography
Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure of merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package, QPtomographer, implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Our tools can be used to reliably certify the performance of, e.g., error correction codes, implementations of unitary gates, or more generally any noise process affecting a quantum system
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