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Verifiable Relativistic Quantum Communication

Yadong Wu

Published Nov 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.11575/prism/37239

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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.
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.
In quantum secret sharing protocols, the usual presumption is that the distribution of quantum shares and players' collaboration are both performed inertially. Here we develop a quantum secret sharing protocol that relaxes these assumptions wherein we consider the effects due to the accelerating motion of the shares. Specifically, we solve the (2,3)-threshold continuous-variable quantum secret sharing in noninertial frames. To this aim, we formulate the effect of relativistic motion on the quantum field inside a cavity as a bosonic quantum Gaussian channel. We investigate how the fidelity of quantum secret sharing is affected by nonuniform motion of the quantum shares. Furthermore, we fully characterize the canonical form of the Gaussian channel, which can be utilized in quantum-information-processing protocols to include relativistic effects.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.
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.
We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.
We introduce a relativistic version of quantum encryption protocol by considering two inertial observers who wish to securely transmit quantum information encoded in a free scalar quantum field state forming Minkowski particles. In a non-relativistic setting a certain amount of shared classical resources is necessary to perfectly encrypt the state. We show that in the case of a uniformly accelerated eavesdropper the communicating parties need to share (asymptotically in the limit of infinite acceleration) just half of the classical resources.