Related papers: Approximating quantum channels by completely posit…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
A unital completely positive map governing the time evolution of a quantum system is usually called a quantum channel, and it can be represented by a tuple of operators which are then referred to as the Kraus operators of the channel. We…
The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation,…
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…
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.…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
Let G be a finite subgroup of unitary matrices acting on the space of $N$-qubits. We associate with G a uniform quantum channel QU from the space on $N$-qubits to itself. We give a quantum algorithm to approximate this channel by…
We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be…
We show that any incoherent qubit channel could be decomposed into four incoherent Kraus operators. The proof consists in showing existence of four incoherent Kraus operators by decomposing the corresponding Choi-Jamio\l{}kowski-Sudarshan…
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…
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…
The corrected capacity of a quantum channel is defined as the best one-shot capacity that can be obtained by measuring the environment and using the result to correct the output of the channel. It is shown that (i) all qubit channels have…
We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…
We study the estimation of an unknown quantum channel $\mathcal{E}$ with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. We establish a connection between the query complexities in two models: (i) access to…
In this paper we study diagonal quantum channels and their structure by proving some results and giving most applicable instances of them. Firstly, it is shown that action of every diagonal quantum channel on pure state from computational…
Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a non-infinitesimal time resolution. In this work, we propose a systematic…
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…