The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the test states used in quantum benchmarking experiments may be imperfect as well. Many quantum benchmarks are only valid for states which match some ideal form, such as pure states or Gaussian states. We outline how to perform quantum benchmarking using arbitrary states of light. We demonstrate these results using real data taken from a continuous-variable quantum memory.
The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the test states used in quantum benchmarking experiments may be imperfect as well. Many quantum benchmarks are only valid for states which match some ideal form, such as pure states or Gaussian states. We outline how to perform quantum benchmarking using arbitrary states of light. We demonstrate these results using real data taken from a continuous-variable quantum memory.
In this thesis, we develop a number of operational tests and tools for benchmarking the quantum nature of optical quantum communication devices. Using the laws of quantum physics, ideal quantum devices can fundamentally outperform their classical counterparts, or even achieve objectives which are classically impossible. Actual devices will not be ideal, but they may still be capable of facilitating quantum communication. Benchmarking tests, based on the presence of entanglement, can be used to verify whether or not imperfect quantum devices offer any advantage over their classical analogs. The general goal in this thesis is to provide strong benchmarking tools which simultaneously require minimal experimental resources but also offer a wide range of applicability. Another major component is the extension of existing qualitative benchmarks (`Is it quantum or classical?') to more quantitative forms (`How quantum is it?'). We provide a number of benchmarking results applicable to two main situations, namely discrete remote state preparation protocols and continuous-variable quantum device testing. The theoretical tools derived throughout this thesis are also applied to the tasks of certifying a remote state preparation experiment and a continuous-variable quantum memory.
Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.
Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large-scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.
Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify that such devices retain their quantum advantages. Benchmarks based on witnessing entanglement have proven useful for verifying the true quantum nature of these devices. The next challenge is to characterize how strongly a device is within the quantum domain. We present a method, based on entanglement measures and rigorous state truncation, which allows us to characterize the degree of quantumness of optical devices. This method serves as a quantitative extension to a large class of previously known quantum benchmarks, requiring no additional information beyond what is already used for the nonquantitative benchmarks.
Current communication networks are based on classical physics and classical information-processing. However, for nearly a century, we have known that at its most fundamental level, the universe is governed by the laws of quantum mechanics. With quantum communication, new possibilities arise in our capabilities to transmit and process information which, in many cases, lead to advantages compared to what is classically possible. The entire scope of tasks for which quantum communication can offer improvements has not yet been fully explored, but several quantum protocols are known that can either perform tasks which are impossible with classical resources or can outperform classical protocols. These quantum protocols are well understood from a theoretical point of view, but many of them have never been demonstrated in practice. Thus, in the context of quantum communication, there is a significant gap between theory and experiment that must be removed in order to harness the advantages provided by quantum mechanics in a practical setting. \n \nIn this thesis, we develop a series of tools for developing and testing practical quantum communication protocols. Our main technique is a theoretical reformulation of existing quantum communication protocols that converts them into a form in which they can be demonstrated with existing experimental techniques. More precisely, they can be implemented using only coherent states of light and linear optics circuits while still retaining the crucial properties of the original abstract protocols. We use this result to construct practical protocols for the Hidden Matching problem and quantum fingerprinting. \n \n \nIn the case of quantum fingerprinting, we make a thorough analysis of the role played by experimental errors and show that our practical protocol can still be implemented in the presence of these imperfections. In fact, we report a proof of concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best known classical protocol for this problem. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. \n \nSimilarly, in the context of cryptography, we propose a multiparty quantum signature protocol that can be implemented from any point-to-point quantum key distribution network, proving its security against forging, repudiation and non-transferability. Crucially, since quantum key distribution is already a practical technology, so is this protocol. However, unlike other tasks in quantum communication, there has not been significant theoretical work on establishing a security model for quantum signature schemes. Consequently, we also constructed a security framework for these schemes and proved several properties that these protocols must satisfy in order to achieve their security goals. \n \nFinally, in addition to proposing new practical protocols, we provide a reliable data analysis technique to verify an important property of many quantum communication protocols: the presence of entanglement. Our technique is based on entanglement witnesses and it does not require the specification of a prior distribution nor the assumption of independent measurements. The technique is suitable to be used with nonlinear entanglement witnesses, which we show can be constructed from any linear witness and evaluated from the same experimental data. We also develop numerical tools necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.