Related papers: On almost randomizing channels with a short Kraus …
In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of probability distributions is described. The sufficient condition…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
In this work, we prove a lower bound on the difference between the first and second singular values of quantum channels induced by random isometries, that is tight in the scaling of the number of Kraus operators. This allows us to give an…
We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In…
We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states.…
Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schr\"odinger operator on the complete graph. The operators exhibits…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
We present a quantum circuit that implements the random dilation superchannel, transforming parallel queries of an unknown quantum channel into the same number of parallel queries of a randomly chosen dilation isometry of the input channel.…
We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically,…
We prove that if any error channel has a Kraus decomposition that is simultaneously correctable and Hilbert-Schmidt (HS) complete, then the existence of Kraus sets with these properties guarantees the correctability of all quantum channels.…
Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic…
The fragile nature of quantum information makes it practically impossible to completely isolate a quantum state from noise under quantum channel transmissions. Quantum networks are complex systems formed by the interconnection of quantum…
This paper deals with the entanglement, as quantified by the negativity, of pure quantum states chosen at random from the invariant Haar measure. We show that it is a constant (0.72037) multiple of the maximum possible entanglement. In line…
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual…
Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes…
This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an…
Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.…
Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…