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G. Chiribella

Publications and source records attributed to G. Chiribella.

35 records · Page 2Linked to original sources
arXiv2008

Optimal covariant quantum networks

A sequential network of quantum operations is efficiently described by its quantum comb, a non-negative operator with suitable normalization constraints. Here we analyze the case of networks enjoying symmetry with respect to the action of a given group of physical transformations, introducing the notion of covariant combs and testers, and proving the basic structure theorems for these objects. As an application, we discuss the optimal alignment of reference frames (without pre-established common references) with multiple rounds of quantum communication, showing that i) allowing an arbitrary amount of classical communication does not improve the alignment, and ii) a single round of quantum communication is sufficient.

quant-ph↗
arXiv2008

Transforming quantum operations: quantum supermaps

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

quant-ph↗
arXiv2008

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.

math-ph↗
arXiv2007

Realization of continuous-outcome measurements on finite dimensional quantum systems

This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with continuous set of outcomes can be simply realized by randomizing some classical parameter and conditionally performing a measurement with finite outcomes.

quant-ph↗
arXiv2007

Quantum information becomes classical when distributed to many users

Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order 1/M. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has error probability p > 0.45 in distinguishing classical from quantum output--a value close to the error probability of the random guess.

quant-ph↗
arXiv2006

Quantum erasure of decoherence

We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction. Moreover, we present the generalization of the eraser setup for d-dimensional systems, showing that any von Neumann measurement on a system can be undone by a complementary measurement on the environment.

quant-ph↗
arXiv2006

Applications of the group SU(1,1) for quantum computation and tomography

This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of elementary gates, and the second is about the regularization of group identities for tomographic purposes.

quant-ph↗
arXiv2006

Superbroadcasting and classical information

We address the problem of broadcasting N copies of a generic qubit state to M>N copies by estimating its direction and preparing a suitable output state according to the outcome of the estimate. This semiclassical broadcasting protocol is more restrictive than a general one, since it requires an intermediate step where classical information is extracted and processed. However, we prove that a suboptimal superbroadcasting, namely broadcasting with simultaneous purification of the local output states with respect to the input ones, is possible. We show that in the asymptotic limit of $M \to \infty$ the purification rate converges to the optimal one, proving the conjecture that optimal broadcasting and state estimation are asymptotically equivalent. We also show that it is possible to achieve superbroadcasting with simultaneous inversion of the Bloch vector direction (universal NOT). We prove that in this case the semiclassical procedure of state estimation and preparation turns out to be optimal. We finally analyse semiclassical superbroadcasting in the phase-covariant case.

quant-ph↗
arXiv2006

Extremal covariant measurements

We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is generally non-transitive. In this case the POVM density is made of multiple orbits of positive operators, and, in the case of extremal measurements, we provide a bound for the number of orbits and for the rank of POVM elements. Two relevant applications are considered, concerning state discrimination with mutually unbiased bases and the maximization of the mutual information.

quant-ph↗
arXiv2006

Joint estimation of real squeezing and displacement

We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we provide a solution for the problem of estimating the unknown unitary action of a nonunimodular group in the maximum likelihood approach. Remarkably, in this case the optimal measurements do not coincide with the so called square-root measurements. In the case of squeezing and displacement we analyze in detail the sensitivity of estimation for coherent states and displaced squeezed states, deriving the asymptotic relation between the uncertainties in the joint estimation and the corresponding uncertainties in the optimal separate measurements of squeezing and displacement. A two-mode setup is also analyzed, showing how entanglement between optical modes can be used to approximate perfect estimation.

quant-ph↗
arXiv2006

Optimal estimation of squeezing

We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the r.m.s. of the estimation scales as $(2\sqrt {\bar n})^{-1}$ versus the average photon number $\bar n$, while it can be enhanced to $(2\bar n)^{-1}$ by using displaced squeezed states.

quant-ph↗
arXiv2005

Optimal estimation of group transformations using entanglement

We derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. A first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N).

quant-ph↗
arXiv2005

Extremal quantum cloning machines

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are "extremal" in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called "double-Bell states", whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our result can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacements.

quant-ph↗
arXiv2005

Maximum likelihood estimation for a group of physical transformations

The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide a deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appear to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

quant-ph↗
arXiv2004

Efficient use of quantum resources for the transmission of a reference frame

We propose a covariant protocol for transmitting reference frames encoded on $N$ spins, achieving sensitivity $N^{-2}$ without the need of a pre-established reference frame and without using entanglement between sender and receiver. The protocol exploits the use of equivalent representations, which were overlooked in the previous literature.

quant-ph↗