Electromagnetic channel capacity for practical purposes

We give analytic upper bounds to the channel capacity C for transmission of classical information in electromagnetic channels (bosonic channels with thermal noise). In the practically relevant regimes of high noise and low transmissivity, by comparison with know lower bounds on C, our inequalities determine the value of the capacity up to corrections which are irrelevant for all practical purposes. Examples of such channels are radio communication, infrared or visible-wavelength free space channels. We also provide bounds to active channels that include amplification.Comment: 6 pages, 3 figures. NB: the capacity bounds are constructed by generalizing to the multi-mode case the minimum-output entropy bounds of arXiv:quant-ph/0404005 [Phys. Rev. A 70, 032315 (2004)

Quantum parallel dense coding of optical images

We propose quantum dense coding protocol for optical images. This protocol extends the earlier proposed dense coding scheme for continuous variables [S.L.Braunstein and H.J.Kimble, Phys.Rev.A 61, 042302 (2000)] to an essentially multimode in space and time optical quantum communication channel. This new scheme allows, in particular, for parallel dense coding of non-stationary optical images. Similar to some other quantum dense coding protocols, our scheme exploits the possibility of sending a classical message through only one of the two entangled spatially-multimode beams, using the other one as a reference system. We evaluate the Shannon mutual information for our protocol and find that it is superior to the standard quantum limit. Finally, we show how to optimize the performance of our scheme as a function of the spatio-temporal parameters of the multimode entangled light and of the input images.Comment: 15 pages, 4 figures, RevTeX4. Submitted to the Special Issue on Quantum Imaging in Journal of Modern Optic

A generalization of the Entropy Power Inequality to Bosonic Quantum Systems

In most communication schemes information is transmitted via travelling modes of electromagnetic radiation. These modes are unavoidably subject to environmental noise along any physical transmission medium and the quality of the communication channel strongly depends on the minimum noise achievable at the output. For classical signals such noise can be rigorously quantified in terms of the associated Shannon entropy and it is subject to a fundamental lower bound called entropy power inequality. Electromagnetic fields are however quantum mechanical systems and then, especially in low intensity signals, the quantum nature of the information carrier cannot be neglected and many important results derived within classical information theory require non-trivial extensions to the quantum regime. Here we prove one possible generalization of the Entropy Power Inequality to quantum bosonic systems. The impact of this inequality in quantum information theory is potentially large and some relevant implications are considered in this work

Entropy on Spin Factors

Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher. In this paper we will study the properties of Bregman divergences for convex bodies of rank 2. The two most important convex bodies of rank 2 can be identified with the bit and the qubit. We demonstrate that if a convex body of rank 2 has a Bregman divergence that satisfies sufficiency then the convex body is spectral and if the Bregman divergence is monotone then the convex body has the shape of a ball. A ball can be represented as the state space of a spin factor, which is the most simple type of Jordan algebra. We also study the existence of recovery maps for Bregman divergences on spin factors. In general the convex bodies of rank 2 appear as faces of state spaces of higher rank. Therefore our results give strong restrictions on which convex bodies could be the state space of a physical system with a well-behaved entropy function.Comment: 30 pages, 6 figure

Random qubit-states and how best to measure them

We consider the problem of measuring a single qubit, known to have been prepared in either a randomly selected pure state or a randomly selected real pure state. We seek the measurements that provide either the best estimate of the state prepared or maximise the accessible information. Surprisingly, any sensible measurement turns out to be optimal. We discuss the application of these ideas to multiple qubits and higher-dimensional systems

Classical communication and non-classical fidelity of quantum teleportation

In quantum teleportation, the role of entanglement has been much discussed. It is known that entanglement is necessary for achieving non-classical teleportation fidelity. Here we focus on the amount of classical communication that is necessary to obtain non-classical fidelity in teleportation. We quantify the amount of classical communication that is sufficient for achieving non-classical fidelity for two independent 1-bit and single 2-bits noisy classical channels. It is shown that on average 0.208 bits of classical communication is sufficient to get non-classical fidelity. We also find the necessary amount of classical communication in case of isotropic transformation. Finally we study how the amount of sufficient classical communication increases with weakening of entanglement used in the teleportation process.Comment: Accepted in Quantum Info. Proces

Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position

On the notion of composite system

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.Comment: 9 pages. Comments are welcom

Information-theoretic postulates for quantum theory

Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary of our paper [New J. Phys. 13, 063001, 2011] addressing these questions, presenting the main ideas, but dropping many technical details. We show that the formalism of quantum theory can be reconstructed from four natural postulates, which do not refer to the mathematical formalism, but only to the information-theoretic content of the physical theory. Our starting point is to assume that there exist physical events (such as measurement outcomes) that happen probabilistically, yielding the mathematical framework of "convex state spaces". Then, quantum theory can be reconstructed by assuming that (i) global states are determined by correlations between local measurements, (ii) systems that carry the same amount of information have equivalent state spaces, (iii) reversible time evolution can map every pure state to every other, and (iv) positivity of probabilities is the only restriction on the possible measurements.Comment: 17 pages, 3 figures. v3: some typos corrected and references updated. Summarizes the argumentation and results of arXiv:1004.1483. Contribution to the book "Quantum Theory: Informational Foundations and Foils", Springer Verlag (http://www.springer.com/us/book/9789401773027), 201

Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity

As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist pairs of discrete memoryless quantum channels, each of zero quantum capacity, which acquire positive quantum capacity when used together. Here we show that this "superactivation" phenomenon also occurs in the more realistic setting of optical channels with attenuation and Gaussian noise. This paves the way for its experimental realization and application in real-world communications systems.Comment: 5 pages, 4 figures, one appendi