Extremal covariant POVM's

We consider the convex set of positive operator valued measures (POVM) which are covariant under a finite dimensional unitary projective representation of a group. We derive a general characterization for the extremal points, and provide bounds for the ranks of the corresponding POVM densities, also relating extremality to uniqueness and stability of optimized measurements. Examples of applications are given.Comment: 15 pages, no figure

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.Comment: 10 pages, 3 figure

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.Comment: 4 pages, no figures, published versio

No-signaling, entanglement-breaking, and localizability in bipartite channels

A bipartite quantum channel represents the interaction between systems, generally allowing for exchange of information. A special class of bipartite channels are the no-signaling ones, which do not allow communication. In Ref. [1] it has been conjectured that all no-signaling channels are mixtures of entanglement-breaking and localizable channels, which require only local operations and entanglement. Here we provide the general realization scheme, giving a counterexample to the conjecture.Comment: 4 pages, revtex

Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device

We present the first full experimental quantum tomographic characterization of a single-qubit device achieved with a single entangled input state. The entangled input state plays the role of all possible input states in quantum parallel on the tested device. The method can be trivially extended to any n-qubits device by just replicating the whole experimental setup n times.Comment: 4 pages in revtex4 with 4 eps figure

Efficient universal programmable quantum measurements

A universal programmable detector is a device that can be tuned to perform any desired measurement on a given quantum system, by changing the state of an ancilla. With a finite dimension d for the ancilla only approximate universal programmability is possible, with "size" d=f(1/e) increasing function of the "accuracy" 1/e. In this letter we show that, much better than the exponential size known in the literature, one can achieve polynomial size. An explicit example with linear size is also presented. Finally, we show that for covariant measurements exact programmability is feasible.Comment: 4 pages, RevTex

Superbroadcasting of mixed states

We derive the optimal universal broadcasting for mixed states of qubits. We show that the nobroadcasting theorem cannot be generalized to more than a single input copy. Moreover, for four or more input copies it is even possible to purify the input states while broadcasting. We name such purifying broadcasting superbroadcasting.Comment: 4 pages, 4 figures, to appear on Phys. Rev. Let

Imprinting a complete information about a quantum channel on its output state

We introduce a novel property of bipartite quantum states, which we call "faithfulness", and we say that a state is faithful when acting with a channel on one of the two quantum systems, the output state carries a complete information about the channel. The concept of faithfulness can also be extended to sets of states, when the output states patched together carry a complete imprinting of the channel.Comment: revtex4, 4 pages, submitted to PR

Quantum error correction with degenerate codes for correlated noise

We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by exhibiting examples where the quantum packing bound is violated.Comment: 5 pages, published versio

Optimal Time-Reversal of Multi-phase Equatorial States

Even though the time-reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common de-phasing in a n-level system. However, in the presence of multiple phases (i. e. a different de-phasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time-reversal of multi-phase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the Universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time-reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement/preparation procedure. Unitary realizations of the optimal time-reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.Comment: 7 pages, minor change