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arXiv:2105.13823

Hacking Quantum Networks: Extraction and Installation of Quantum Data

Seok Hyung Lie, Yong Siah Teo, Hyunseok Jeong

Published May 28, 2021• 0 citations
arXivHTMLPDF

Abstract

We study the problem of quantum hacking, which is the procedure of quantum-information extraction from and installation on a quantum network given only partial access. This problem generalizes a central topic in contemporary physics -- information recovery from systems undergoing scrambling dynamics, such as the Hayden--Preskill protocol in black-hole studies. We show that a properly prepared partially entangled probe state can generally outperform a maximally entangled one in quantum hacking. Moreover, we prove that finding an optimal decoder for this stronger task is equivalent to that for Hayden--Preskill-type protocols, and supply analytical formulas for the optimal hacking fidelity of large networks. In the two-user scenario where Bob attempts to hack Alice's data, we find that the optimal fidelity increases with Bob's hacking space relative to Alice's user space. However, if a third neutral party, Charlie, is accessing the computer concurrently, the optimal hacking fidelity against Alice drops with Charlie's user-space dimension, rendering targeted quantum hacking futile in high-dimensional multi-user scenarios without classical attacks. When applied to the black-hole information problem, the limited hacking fidelity implies a reflectivity decay of a black hole as an information mirror.

DOI
10.48550/arxiv.2105.13823

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We study the problem of quantum hacking, which is the procedure of quantum-information extraction from and installation on a quantum network given only partial access. This problem generalizes a central topic in contemporary physics -- information recovery from systems undergoing scrambling dynamics, such as the Hayden--Preskill protocol in black-hole studies. We show that a properly prepared partially entangled probe state can generally outperform a maximally entangled one in quantum hacking. Moreover, we prove that finding an optimal decoder for this stronger task is equivalent to that for Hayden--Preskill-type protocols, and supply analytical formulas for the optimal hacking fidelity of large networks. In the two-user scenario where Bob attempts to hack Alice's data, we find that the optimal fidelity increases with Bob's hacking space relative to Alice's user space. However, if a third neutral party, Charlie, is accessing the computer concurrently, the optimal hacking fidelity against Alice drops with Charlie's user-space dimension, rendering targeted quantum hacking futile in high-dimensional multi-user scenarios without classical attacks. When applied to the black-hole information problem, the limited hacking fidelity implies a reflectivity decay of a black hole as an information mirror.
We introduce and study the problem of scrambler hacking, which is the procedure of quantum information extraction from and installation on a quantum scrambler given only partial access. This problem necessarily emerges from a central topic in contemporary physics - information recovery from systems undergoing scrambling dynamics, such as the Hayden-Preskill protocol in black hole studies - because one must replace quantum data with another when extracting it due to the no-cloning theorem. For large scramblers, we supply analytical formulas for the optimal hacking fidelity, a quantitative measure of the effectiveness of scrambler hacking with limited access. In the two-user scenario where Bob attempts to hack Alice's data, we find that the optimal fidelity converges to 64/(9π2)≈0.7264/(9π^2)\approx0.7264/(9π2)≈0.72 with increasing Bob's hacking space relative to Alice's user space. We applied our results to the black hole information problem and showed that the limited hacking fidelity implies the reflectivity decay of a black hole as an information mirror, which questions the solvability of the black hole information paradox through the Hayden-Preskill type protocol.
We study the problem of extracting EPR pairs from a general source of entanglement. Suppose Alice and Bob share a bipartite state R which is reasonably to perfect EPR pairs. The only information Alice and Bob possess is a lower bound on the fidelity of R and a maximally entangled state. They wish to purify R using local operations and classical communication and output a state that is arbitrarily close to EPR pairs. We prove that on average, Alice and Bob cannot increase the fidelity of the input state significantly. On the other hand, there exist that may fail with a small probability, and otherwise will output states arbitrarily close to EPR pairs with very high probability. These come from the purity-testing protocols of Barnum et al.
Hayden and Preskill proposed a thought experiment in which Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and for which Yoshida and Kitaev recently proposed a concrete decoding scheme.In the context of quantum many-body physics, the parallel question is that after a small system is thermalized with a large system, how can one decode the initial state information with the help of two entangled many-body systems?Here, we propose to realize this decoding protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state.We show that the Yoshida-Kitaev protocol allows us to read out the initial spin information after it is scrambled into the cavity.We show that the readout efficiency reaches a maximum when the model parameters are tuned to the regime where the system is the most chaotic, characterized by the shortest scrambling time in the out-of-time-ordered correlation function.Our proposal opens up the possibility of discussing this profound thought experiment in a realistic setting.
According to recent estimates, 10^18 bytes of data are generated on a daily basis around the globe. Our information society urges for radical solutions to treat such data deluge. By exploiting fundamental key elements of quantum theory -arguably the most probed theory of modern physics- quantum information science is nowadays revolutionizing the way in which we acquire, process, store and transmit information. In the midst of the information era, the potential of quantum technologies is being recognized by the industry sector, and in turn, new capabilities for quantum information processing keep driving exciting discoveries related to more fundamental aspects of science. There are several research programs all around the world fostering the development and commercialization of quantum technologies, mostly for cryptographic and randomness generation duties. Thus, the technological limitations that today step us aside from the quantum information era are gradually being overcome. But there is a fundamental issue that still needs to be faced: the impossibility to know what is really going on in quantum experiments, due to their atomic-scale dimensions. Indeed, how will an average user guarantee the proper functioning of a quantum device that has been purchased from an external company? To his eyes, the device will merely look like a black box. Even if the customer holds a PhD in quantum science, the issue will remain fundamentally cumbersome because of the impossibility to fully control, i.e. monitor, all the physical processes occurring in any quantum experiment. Furthermore, the situation turns even more dramatic when considering adversarial applications, where a malicious eavesdropper could break the devices to manipulate their internal working, turning the protocol insecure and hence irrelevant as well. Therefore, it is the purpose of this Thesis to contribute to the experimental development of quantum information protocols with uncharacterized devices, namely, device-independent quantum information protocols. These protocols are naturally immune to any attack or failure related to mismatches between protocol theory and its actual implementation. This is achieved throughout the different Chapters by pursuing the following three overlapping duties: (i) To broaden theoretic capabilities by establishing a richer understanding of relevant fundamental resources lying at the basis of the theory of quantum information with uncharacterized devices. (ii) To develop competitive quantum information protocols by finding an adequate trade-off between high-performance and practicability; between the power of the device-independent framework and its less demanding, so-called semi-device-independent, relaxations. (iii) To analyze and improve experimental conditions of diverse physical setups in order to carry out implementations in proof-of-principle experiments demonstrating quantum information protocols with black boxes. Our objective of turning the theory of quantum information into a graspable technology for our society through the development and implementation of protocols based on the minimalist, user-friendly, black-box paradigm contributes not only to the technological development of these protocols, but it also offers valuable insights on more fundamental aspects of quantum theory. In this sense, we contribute to the characterization and quantification of entanglement -the pivotal quantum resource at the basis of most testable phenomena without classical account- in scenarios of practical interest where uncharacterized devices are used. From the more applied perspective, we contribute to the development of two specific information tasks: the certification of genuinely random numbers in device-independent and semi-device-independent scenarios, and the generation of a shared secret key among two parties in a full device-independent manner. De acuerdo con estimaciones recientes, 10^18 bytes de datos se generan diariamente alrededor del mundo. Nuestra sociedad necesita urgentemente soluciones efectivas para lidiar con este diluvio de datos. Utilizando elementos fundamentales de la teoría cuántica -la teoría más explorada de la física moderna, posiblemente- la información cuántica está revolucionando la forma en la que adquirimos, procesamos, almacenamos y transmitimos información. En plena era de la información, el sector industrial reconoce cada vez más el potencial de las tecnologías cuánticas, y a su vez nuevos desarrollos en el procesamiento de la información cuántica continúan impulsando descubrimientos prominentes relacionados con aspectos científcos de carácter más fundamental. Existen varios programas de investigación alrededor del mundo desarrollando y comercializando tecnologías cuánticas, principalmente para aplicaciones de criptografía y generación de números aleatorios. Así, las limitaciones que hoy nos separan de la era de la información cuántica están siendo gradualmente superadas. Sin embargo, existe un problema fundamental que aún necesita ser enfrentado: la imposibilidad de saber lo que realmente sucede en un experimento cuántico, debido a sus dimensiones de tamaño atómico. En efecto, ¿cómo podrá un usuario garantizar el funcionamiento adecuado de un dispositivo cuántico que ha sido adquirido a través de una compañía externa? A sus ojos el dispositivo será una verdadera caja negra. Incluso si el usuario contara con un Doctorado en ciencia cuántica, el problema prevalecería insoluble debido a la imposibilidad de controlar a la perfección, es decir monitorear, todos los procesos físicos que ocurren en cualquier experimento cuántico. Además, la situación se vuelve aún más dramática si se piensa en aplicaciones en donde un agente maligno pudiese hackear los dispositivos y manipular su funcionamiento interno, volviendo así el protocolo en cuestión inseguro y por ende también irrelevante. El propósito de esta Tesis es entonces contribuir al desarrollo experimental de protocolos de información cuántica con dispositivos sin caracterizar, llamados "device-independent". Estos protocolos son, por naturaleza, immunes a cualquier ataque o falla relacionada con desajustes entre la teoría y la implementación del protocolo. Esto se logra a lo largo de los diferentes Capítulos prosiguiendo las siguientes tres tareas que en ocasiones se traslapan: (i) Ampliar las capacidades teóricas estableciendo un entendimiento mayor de los recursos fundamentales de la teoría de la información cuántica con dispositivos sin caracterizar. (ii) Desarrollar protocolos de información cuántica competitivos, encontrando un intercambio adecuado entre alto rendimiento y practicabilidad; entre el poder del marco de trabajo device-independent y sus menos demandantes versiones, dichas "semi-device-independent". (iii) Analizar y mejorar las condiciones experimentales de diversas plataformas para llevar a cabo implementaciones en experimentos de prueba de principio, demostrando la realización de protocolos de información cuántica con cajas negras. 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We study the Hayden-Preskill thought experiment at finite temperature and obtain the decoupling condition that the information thrown into an old black hole can be extracted by decoding the Hawking radiation. We then consider the decoding Hayden-Preskill protocol at finite temperature assuming the observer outside the black hole who has the access to the full radiation and the unitary dynamics of the black hole. We also consider the cases when the Hawking radiation has noise and decoherence in the storage. The decoding probabilities and the corresponding fidelities are calculated. It is shown that for all the three cases we have considered, the decoding fidelities are less than unity in general. This result indicates that at finite temperature, the decoding strategy and the recovery algorithm are harder to realize than that at infinite temperature.
This paper investigates the core methods of information encoding and decoding within quantum networks, aiming to enhance both the efficiency and security of quantum information transmission. We explore various encoding schemes, including amplitude encoding, phase encoding, and polarization encoding, alongside their corresponding decoding strategies. The core mechanism relies on manipulating quantum states to represent and transmit information securely. Our research focuses on optimizing these processes to mitigate the effects of noise and loss, critical challenges in long-distance quantum communication. We delve into error correction techniques specifically tailored for quantum systems, such as quantum error correction codes (QECCs) and their application in decoding. Furthermore, we examine the role of quantum key distribution (QKD) protocols as a fundamental decoding process, highlighting the security aspects derived from the laws of quantum mechanics. The ultimate goal is to provide a comprehensive overview of the current state-of-the-art in quantum network information encoding and decoding, paving the way for future advancements in quantum communication technologies.