Criteria for Continuous-Variable Quantum Teleportation

We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of $0.58 \pm 0.02$ was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.Comment: 12 pages, to appear in Journal of Modern Optic

Maximization of capacity and p-norms for some product channels

It is conjectured that the Holevo capacity of a product channel \Omega \otimes \Phi is achieved when product states are used as input. Amosov, Holevo and Werner have also conjectured that the maximal p-norm of a product channel is achieved with product input states. In this paper we establish both of these conjectures in the case that \Omega is arbitrary and \Phi is a CQ or QC channel (as defined by Holevo). We also establish the Amosov, Holevo and Werner conjecture when \Omega is arbitrary and either \Phi is a qubit channel and p=2, or \Phi is a unital qubit channel and p is integer. Our proofs involve a new conjecture for the norm of an output state of the half-noisy channel I \otimes \Phi, when \Phi is a qubit channel. We show that this conjecture in some cases also implies additivity of the Holevo capacity

Optimal signal states for quantum detectors

Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question of fundamental significance is how much information a quantum detector can extract from the quantum system it is applied to. In the present paper we address this question within a precise framework: given a quantum detector implementing a specific generalized quantum measurement, what is the optimal performance achievable with it for a concrete information readout task, and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks - the Bayes cost problem (of which minimal error discrimination is a special case), unambiguous message discrimination, and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information has an interpretation of a capacity of the measurement, and derive various properties that it satisfies, including its relation to the accessible information of an ensemble of states, and its form in the case of a group-covariant measurement. We illustrate our results with the example of a noisy two-level symmetric informationally complete measurement, for whose capacity we give analytical proofs of optimality. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.Comment: 13 pages, 1 figure, example section extende

Nonsemisimple Fusion Algebras and the Verlinde Formula

We find a nonsemisimple fusion algebra F_p associated with each (1,p) Virasoro model. We present a nonsemisimple generalization of the Verlinde formula which allows us to derive F_p from modular transformations of characters.Comment: LaTeX (amsart, xypic, times), 35p

Nonorthogonal Quantum States Maximize Classical Information Capacity

I demonstrate that, rather unexpectedly, there exist noisy quantum channels for which the optimal classical information transmission rate is achieved only by signaling alphabets consisting of nonorthogonal quantum states.Comment: 5 pages, REVTeX, mild extension of results, much improved presentation, to appear in Physical Review Letter