相关论文: Extremal equation for optimal completely-positive …
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by M. Hayashi in terms of an infinite set of covariant…
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…
We consider the convex set of ( unital ) positive ( completely ) maps from a $C^*$ algebra $\cla$ to a von-Neumann sub-algebra $\clm$ of $\clb(\clh)$, the algebra of bounded linear operators on a Hilbert space $\clh$ and study its extreme…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where…
We consider the problem of identifying the quantum spin states that are the optimal sensors of a given transformation averaged over all possible orientations of the spin system. Our geometric approach to the problem is based on a fidelity…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state…
The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the…
We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions…
Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms.…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…