Related papers: The Quantum Blackwell Theorem and Minimum Error St…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
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…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear…
We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…
A stochastic process's statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a…
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a…
Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and…
We introduce a method for testing quantum correlations in terms of quasiprobability functions in the presence of noise. We analyze the effects of measurement imperfection and thermal environment on quantum correlations and show that their…
We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the…
To establish an entangled state of optimal fidelity between two distant observers when the available quantum channel is noisy, is a central problem in quantum information theory. We consider an instance of this problem for two-qubit systems…
We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original…
Bell type inequalities are used to test local realism against quantum theory.In this paper, we consider a two party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated…
The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the…
In order to understand the capabilities and limitations of quantum computers, it is necessary to develop methods that efficiently characterize and benchmark error channels present on these devices. In this paper, we present a method that…
Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a…
We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states, and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously…
We present an uncertainty-relation-type quantum benchmark for continuous-variable (CV) quantum channels that works with an input ensemble of Gaussian distributed coherent states and homodyne measurements. It determines an optimal trade-off…
Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…