Strong converse rates for classical communication over thermal and additive noise bosonic channels

We prove that several known upper bounds on the classical capacity of thermal and additive noise bosonic channels are actually strong converse rates. Our results strengthen the interpretation of these upper bounds, in the sense that we now know that the probability of correctly decoding a classical message rapidly converges to zero in the limit of many channel uses if the communication rate exceeds these upper bounds. In order for these theorems to hold, we need to impose a maximum photon number constraint on the states input to the channel (the strong converse property need not hold if there is only a mean photon number constraint). Our first theorem demonstrates that Koenig and Smith's upper bound on the classical capacity of the thermal bosonic channel is a strong converse rate, and we prove this result by utilizing the structural decomposition of a thermal channel into a pure-loss channel followed by an amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s upper bound on the classical capacity of a thermal bosonic channel corresponds to a strong converse rate, and we prove this result by relating success probability to rate, the effective dimension of the output space, and the purity of the channel as measured by the Renyi collision entropy. Finally, we use similar techniques to prove that similar previously known upper bounds on the classical capacity of an additive noise bosonic channel correspond to strong converse rates.Comment: Accepted for publication in Physical Review A; minor changes in the text and few reference

Topics in Quantum Metrology, Control, and Communications

Noise present in an environment has significant impacts on a quantum system affecting properties like coherence, entanglement and other metrological features of a quantum state. In this dissertation, we address the effects of different types of noise that are present in a communication channel (or medium) and an interferometric setup, and analyze their effects in the contexts of preserving coherence and entanglement, phase sensitivity, and limits on rate of communication through noisy channels. We first consider quantum optical phase estimation in quantum metrology when phase fluctuations are introduced in the system by its interaction with a noisy environment. By considering path-entangled dual-mode photon Fock states in a Mach-Zehnder optical interferometric configuration, we show that such phase fluctuations affect phase sensitivity and visibility by adding noise to the phase to be estimated. We also demonstrate that the optimal detection strategy for estimating a phase in the presence of such phase noise is provided by the parity detection scheme. We then investigate the random birefringent noise present in an optical fiber affecting the coherence properties of a single photon polarization qubit propagating through it. We show that a simple but effective control technique, called dynamical decoupling, can be used to suppress the effects of the dephasing noise, thereby preserving its ability to carry the encoded quantum information in a long-distance optical fiber communication system. Optical amplifiers and attenuators can also add noise to an entangled quantum system, deteriorating the non-classical properties of the state. We show this by considering a two-mode squeezed vacuum state, which is a Gaussian entangled state, propagating through a noisy medium, and characterizing the loss of entanglement in the covariance matrix and the symplectic formalism for this state. Finally, we discuss limits on the rate of communication in the context of sending messages through noisy optical quantum communication channels. In particular, we prove that a strong converse theorem holds under a maximum photon number constraint for these channels, guaranteeing that the success probability in decoding the message vanishes in the asymptotic limit for the rate exceeding the capacity of the channels

Ultimate capacity of a linear time-invariant bosonic channel

We determine the ultimate classical information capacity of a linear time-invariant bosonic channel with additive phase-insensitive Gaussian noise. This channel can model fiber-optic communication at power levels below the threshold for significant nonlinear effects. We provide a general continuous-time result that gives the ultimate capacity for such a channel operating in the quasimonochromatic regime under an average power constraint. This ultimate capacity is compared with corresponding results for heterodyne and homodyne detection over the same channel.United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052

Strong converse for the classical capacity of optical quantum communication channels

We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier and free-space communication. The theorem holds under a particular photon-number occupation constraint, which we describe in detail in the paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links.Comment: 15 pages, final version accepted into IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1312.328