Related papers: When is the Chernoff Exponent for Quantum Operatio…
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
We show that the extended Bloch representation of quantum mechanics also applies to infinite-dimensional entities, to the extent that the number of (possibly infinitely degenerate) outcomes of a measurement remains finite, which is always…
Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…
Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to…
The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…
The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
Quantum criticality, being important as an indicator of new quantum matters emerging, is known to occur only at zero or low temperature. We find that a quantum probe, if its coherence time is long, can detect quantum criticality at…
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
As charged particles surpass the speed of light in an optical medium they produce radiation - analogously to the way jet planes surpass the speed of sound and produce a sonic boom. This radiation emission, known as the Cherenkov effect, is…
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication…
We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local…
In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…
We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…
We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses…