Towards a General Framework for Practical Quantum Network Protocols

The quantum internet is one of the frontiers of quantum information science. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement and to guide the realization of large-scale quantum networks, and eventually the quantum internet, especially with the limitations of near-term quantum technologies. This work provides an initial step towards this goal. The main contribution of this thesis is a mathematical framework for entanglement distribution protocols in a quantum network, which allows for discovering optimal protocols using reinforcement learning. We start with a general development of quantum decision processes, which is the theoretical backdrop of reinforcement learning. Then, we define the general task of entanglement distribution in a quantum network, and we present ground- and satellite-based quantum network architectures that incorporate practical aspects of entanglement distribution. We combine the theory of decision processes and the practical quantum network architectures into an overall entanglement distribution protocol. We also define practical figures of merit to evaluate entanglement distribution protocols, which help to guide experimental implementations

Information-theoretic aspects of the generalized amplitude damping channel

The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.Comment: 33 pages, 9 figures; close to the published versio

Symmetric Extendability of Quantum States and the Extreme Limits of Quantum Key Distribution

We investigate QKD protocols with two-way classical post-processing that are based on the well-known six-state and BB84 signal states. In these QKD protocols, the source (Alice) sends quantum signals to the receiver (Bob), who measures them, leaving only classical data on both sides. Our goal is to find the highest value of the quantum bit-error rate (QBER) $Q$ for which two-way classical post-processing protocols on the data can distill secret keys. Using the BB84 signal states, such protocols currently exist for $Q<\frac{1}{5}$. On the other hand, for $Q\geq\frac{1}{4}$ no such protocol can exist as the observed data is compatible with an intercept-resend attack. This leaves the interesting question of whether successful two-way protocols exist in the interval $\frac{1}{5}\leq Q<\frac{1}{4}$. For the six-state signal states, the corresponding interval is known to be $\frac{5-\sqrt{5}}{10}\leq Q<\frac{1}{3}$. We search for two-way protocols because it turns out that within these intervals Alice and Bob's correlations are symmetrically extendable, meaning that Bob and the eavesdropper (Eve) are completely indistinguishable from Alice's point of view, making any one-way Alice-to-Bob post-processing protocol insecure. A two-way protocol might be able to break the symmetry between Bob and Eve, and it must do so in order to distill a secret key because any two-way protocol will necessarily terminate with a one-way communication step, at which point the symmetric extendability of Alice and Bob's updated correlations must be checked again. We first show that the search for two-way protocols breaking the symmetric extendability of Alice and Bob's correlations can be restricted to a search over post-selection protocols if all we care about is whether secret key can at all be distilled and not about the rate of distillation. We then provide strong analytical and numerical evidence to suggest that no two-way classical post-processing protocol exists within the gap when the six-state signal states are used. Under quantum entanglement distillation protocols, it is known that secret key can be distilled right up to the intercept-resend bounds of $\frac{1}{4}$ and $\frac{1}{3}$ for the BB84 and six-state signal states, respectively. We therefore want to know whether classical post-processing protocols are just as good at distilling secret keys as quantum ones. Our results appear to indicate that they are not

A perturbative gadget for delaying the onset of barren plateaus in variational quantum algorithms

Variational quantum algorithms are being explored as a promising approach to finding useful applications for noisy intermediate-scale quantum computers. However, cost functions corresponding to many problems of interest are inherently global, defined by Hamiltonians with many-body interactions. Consequently, the optimization landscape can exhibit exponentially vanishing gradients, so-called barren plateaus, rendering optimal solutions difficult to find. Strategies for mitigating barren plateaus are therefore needed to make variational quantum algorithms trainable and capable of running on larger-scale quantum computers. In this work, we contribute the toolbox of perturbative gadgets to the portfolio of methods being explored in the quest for making noisy intermediate-scale quantum devices useful. We introduce a novel perturbative gadget, tailored to variational quantum algorithms, that can be used to delay the onset of barren plateaus. Our perturbative gadget encodes an arbitrary many-body Hamiltonian corresponding to a global cost function into the low-energy subspace of a three-body Hamiltonian. Our construction requires $rk$ additional qubits for a $k$-body Hamiltonian comprising $r$ terms. We provide guarantees on the closeness of global minima and prove that the local cost function defined by our three-body Hamiltonian exhibits non-vanishing gradients. We then provide numerical demonstrations to show the functioning of our approach and discuss heuristics that might aid its practical implementation.Comment: Added further discussion of the number of required measurement

Fast and reliable entanglement distribution with quantum repeaters: principles for improving protocols using reinforcement learning

Future quantum technologies such as quantum communication, quantum sensing, and distributed quantum computation, will rely on networks of shared entanglement between spatially separated nodes. In this work, we provide improved protocols/policies for entanglement distribution along a linear chain of nodes, both homogeneous and inhomogeneous, that take practical limitations such as photon losses, non-ideal measurements, and quantum memories with short coherence times into account. For a wide range of parameters, our policies improve upon previously known policies, such as the ``swap-as-soon-as-possible'' policy, with respect to both the waiting time and the fidelity of the end-to-end entanglement. This improvement is greatest for the most practically relevant cases, namely, for short coherence times, high link losses, and highly asymmetric links. To obtain our results, we model entanglement distribution using a Markov decision process, and then we use the Q-learning reinforcement learning (RL) algorithm to discover new policies. These new policies are characterized by dynamic, state-dependent memory cutoffs and collaboration between the nodes. In particular, we quantify this collaboration between the nodes. Our quantifiers tell us how much ``global'' knowledge of the network every node has. Finally, our understanding of the performance of large quantum networks is currently limited by the computational inefficiency of simulating them using RL or other optimization methods. Thus, in this work, we present a method for nesting policies in order to obtain policies for large repeater chains. By nesting our RL-based policies for small repeater chains, we obtain policies for large repeater chains that improve upon the swap-as-soon-as-possible policy, and thus we pave the way for a scalable method for obtaining policies for long-distance entanglement distribution.Comment: Version 2, title changed, some typos fixed. 27 pages, 18 figures and 3 tables. Comments are welcom