Amplification, purification and superposition of orders in continuous-variable systems

Abstract

This thesis investigates continuous-variable quantum information processing (CV-QIP) by optimizing some of its basic operations, and by exploring applications of a novel quantum primitive known as indefinite causal order. Specifically, we derive optimization protocols for amplification and purification of noisy coherent states, which are central tasks in CV-QIP. In addition, we explore the application of indefinite causal order to metrology and communication with continuous-variable quantum systems. Our results shed light on the advantages of quantum entanglement, post-selection and indefinite causal order in CV-QIP.

This thesis can be divided into two main parts. In the first part, we establish the optimal quantum protocols for amplification and purification of noisy coherent states with Gaussian modulation. In particular, we determine the ultimate limits achievable by arbitrary quantum operations, in both deterministic and probabilistic scenarios. In the deterministic scenario, we prove that the optimal amplifier of noisy coherent states can be realized by beam-splitters and two-mode squeezing. In the probabilistic scenario, we prove that the optimal amplifier of noisy coherent states can be realized using beam-splitters and the noiseless nondeterministic amplifier proposed by Ralph and Lund. For purification, we find out that probabilistic processes do not offer any advantage over deterministic processes, as long as the input systems are identically prepared. When the input systems are correlated, we show that the optimal probabilistic purifier can beat all deterministic purifiers.

In addition to deriving the optimal quantum processes, we establish the quantum benchmarks that have to be surpassed in order to experimentally demonstrate genuinely quantum amplification and purification. The possibility to surpass the benchmarks shows the advantage of coherent quantum information processing over incoherent measure-and-prepare operations.

In the second part of the thesis, we explore the advantages of indefinite causal order in continuous-variable metrology and communication. Specifically, we demonstrate a quantum advantage in the problem of estimating the product of two average displacements. We prove that every setup where the displacements are used in a fixed order must have a root-mean-square error lower bounded by 1/N, where N is the number of samples used to compute the averages. In stark contrast, we show a setup that uses the displacements in a superposition of orders and yields a root-mean-square error vanishing with inverse quadratic scaling 1/N^2.

We conclude the thesis by extending our investigation of indefinite causal order to continuous-variable quantum communication. First, we show that placing Gaussian additive noise channels in an indefinite causal order yields higher classical capacity than placing them one after the other. Then, we analyze a simulation of the superposition of orders using time-correlated channels, and we find out that certain time-correlations can achieve an even higher capacity than the correlations that simulate the superposition of orders. Our result highlights that the access to time-correlated channels is a strictly stronger resource than the ability to superpose causal orders.