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A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions: the prior existence of a short random seed and the ability to ensure that two black-box devices do not communicate (i.e. are non-signaling). We call protocols achieving such certified amplification of a short random seed randomness amplifiers. We introduce a simple framework in which we initiate the systematic study of the possibilities and limitations of randomness amplifiers. Our main results include a new, improved analysis of a robust randomness amplifier with exponential expansion, as well as the first upper bounds on the maximum expansion achievable by a broad class of randomness amplifiers. In particular, we show that non-adaptive randomness amplifiers that are robust to noise cannot achieve more than doubly exponential expansion. Finally, we show that a wide class of protocols based on the use of the CHSH game can only lead to (singly) exponential expansion if adversarial devices are allowed the full power of non-signaling strategies. Our upper bound results apply to all known non-adaptive randomness amplifier constructions to date.
We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in a
Brand~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the number $m$ of
For the optimal success probability under minimum-error discrimination between $rgeq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these ne
We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructe
We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with quantum battery we refer to the central spins, whereas the bath serves as the charger. For the single central-spin battery,