Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank–Shor–Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Our protocol includes decoding whose gate complexity scales linearly with the number of causal diamonds. Our thorough framework for quantum summoning enables full specification of the protocol, including spatial and temporal implementation and costs, which enables quantum summoning to be a well posed protocol for relativistic quantum communication purposes.
Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank–Shor–Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Our protocol includes decoding whose gate complexity scales linearly with the number of causal diamonds. Our thorough framework for quantum summoning enables full specification of the protocol, including spatial and temporal implementation and costs, which enables quantum summoning to be a well posed protocol for relativistic quantum communication purposes.
Quantum summoning retrieves quantum information prepared at some point in spacetime at another point, which is randomly chosen from a set of points. This thesis presents an efficient quantum summoning protocol based on a quantum error-correcting code, along with encoding and decoding methods. This protocol reduces space complexity as well as gate complexity of encoding compared to previous best results. Our throughout study of quantum summoning paves the way for investigating relativistic quantum cryptography with quantum summoning as a primitive. This thesis also studies a relativistic continuous-variable quantum secret sharing protocol in non-inertial frame, which includes the effect of acceleration of quantum shares in spacetime. By formulating the relativistic effect as a Gaussian lossy channel, we analyze how the fidelity of quantum secret sharing protocol is affected by this relativistic effect. This investigation relaxes the common assumption of secret sharing in inertial frames and this framework can be applied to other relativistic quantum communication protocols. To efficiently verify bosonic quantum channels, I propose a framework of verification of quantum channels plus average-fidelity witness. For both multi-mode Gaussian unitary channels and single-mode amplifying channels, I present efficient verification protocols utilizing only two-mode squeezed vacuum states and homodyne detections. Our work is significant in verification of quantum components in continuous-variable quantum information processing.
Abstract One of the most important properties of quantum information, and the one ultimately responsible for its cryptographic applications, is that it can not be copied. That statement, however, is not completely accurate. While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. We fully characterize which regions of spacetime can all hold the same quantum information. Because quantum information can be delocalized through quantum error correction and teleportation, it need not follow well-defined trajectories. Instead, replication of the information in any configuration of spacetime regions not leading to violations of causality or the no-cloning principle is allowed. To demonstrate this, we answer the operational question of exactly when the information can be summoned to a set of spacetime points, showing how to do so efficiently using a combination of teleportation and codeword-stabilized quantum codes. This provides a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.
Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices' location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries.
The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.
Abstract Wireless communication derives its power from the simultaneous emission of signals in multiple directions. However, in the context of quantum communication, this phenomenon must be reconciled carefully with the no-cloning principle. In this context, we here study how wireless communication of quantum information can be realized via relativistic fields. To this end, we extend existing frameworks to allow for a non-perturbative description of, e.g. quantum state transfer. We consider, in particular, the case of 1+1 spacetime dimensions, which already allows for a number of interesting scenarios, pointing to, for example, new methods for tasks similar to quantum secret sharing.
We show that wireless quantum broadcasting through relativistic quantum fields is impacted by geometry in nontrivial ways that can be traced to the no-cloning principle. To study these phenomena, we extend the framework of models usually employed in the field of relativistic quantum information to allow for the non-perturbative description of, e.g., quantum state transfer. We consider, in particular, the case of 1+1 spacetime dimensions, which already allows a number of interesting scenarios, pointing to, for example, new protocols for quantum secret sharing.