We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels, and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two nonorthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.
We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels, and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two nonorthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.
In this thesis, we investigate the uses of entanglement and its verification in quantum communication. Typically, it is the presence of entanglement which allows quantum communication protocols to outperform their classical counterparts, or to achieve tasks which are infeasible with classical physics. Therefore, the verification of entanglement can provide fundamental tests to certify that experimental implementations of such protocols operate quantum mechanically. The main object here is to develop a verification procedure which is adaptable to a wide range of applications, and whose implementation has low requirements on experimental resources. We present such a procedure in the form of the Expectation Value Matrix. The structure of this thesis is as follows: Chapters 1 and 2 give a short introduction and background information on quantum theory and the quantum states of light. In particular, we discuss the basic postulates of quantum mechanics, quantum state discrimination, the description of quantum light and the homodyne detector. Chapter 3 gives a brief introduction to quantum information and in particular to entanglement, and we discuss the basics of quantum key distribution and teleportation. The general framework of the Expectation Value Matrix is introduced. The main matter of this thesis is contained in the subsequent three chapters, which describe different quantum communication protocols and the corresponding adaptation of the entanglement verification method. The subject of Chapter 4 is quantum key distribution, where the detection of entanglement is a means of excluding intercept-resend attacks, and the presence of quantum correlations in the raw data is a necessary precondition for the generation of secret key. We investigate a continuous-variable version of the two-state protocol and develop the Expectation Value Matrix method for such qubit-mode systems. Furthermore, we analyse the role of the phase reference with respect to the security of the protocol and raise awareness of a corresponding security threat. For this, we adapt the verification method to different settings of Stokes operator measurements. In Chapter 5, we investigate quantum memory channels and propose a fundamental bench- mark for these based on the verification of entanglement. After describing some physical effects which can be used for the coherent storage of light, we focus on the storage of squeezed light. This situation requires an extension of our verification procedure to sources of mixed input states. We propose such an extension, and give a detailed analysis of its application to squeezed thermal states, displaced thermal states and mixed qubit states. This is supplemented by finding the optimal entanglement-breaking channels for each of these situations, which provides us with an indication of the strength of the extension to our entanglement criterion. The subject of Chapter 6 is also the benchmarking of quantum memory or teleportation experiments. Considering a number of recently published benchmark criteria, we investigate the question which one is most useful to actual experiments. For this, a criterion must be both strong, i.e., easy to overcome, and it must be implementable with a reasonable amount of experimental resources. We first compare the different criteria for typical settings and sort them according to their resilience to excess noise. Then, we introduce a further improvement to the Expectation Value Matrix method, which results in the desired optimal benchmark criterion. Finally, we investigate naturally occurring phase fluctuations and find them to further simplify the implementation of our criterion. Thus, we formulate the first truly useful way of validating experiments for the quantum storage or transmission of light.
We consider entanglement detection for quantum-key-distribution systems that use two signal states and continuous-variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testing process for various pure bipartite entangled states up to four dimensions, by simply inspecting the correlations of the measurement outcomes. We show that this self-testing process can certify the exact form of entangled states with fidelities higher than 99.9% for all the investigated scenarios, which indicates the superior completeness and robustness of this method. Our work promotes self-testing as a practical tool for developing quantum techniques.
Abstract Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures.
An optical procedure in the context of continuous variables to verify bipartite entanglement without destroying both systems and their entanglement is proposed. To perform the nondestructive verification of entanglement, the method relies on beam-splitter and quantum nondemolition (QND) interactions of the signal modes with two ancillary probe modes. The probe modes are measured by homodyne detections, and the obtained information is used to feed forward modulation of signal modes, concluding the procedure. Characterizing the method by figures of merit used in QND processes, we can establish the conditions for an effectively quantum scheme. Based on such conditions, it is shown that the classical information acquired from the homodyne detections of probe modes is sufficient to verify the entanglement of the output signal modes. The processing impact due to added noise on the output entanglement is assessed in the case of Gaussian modes.
Practical quantum key distribution can be understood as a two-step procedure: in a first step two parties exchange quantum mechanical signals and perform measurements on them, in a second step auxiliary classical communication protocols are performed over an authenticated public channel to transform the data of the first step into an information-theoretic secure key. In this article we address the question of necessary conditions on the correlated (classical) data of the first step such that there can be a successful second step at all. As it turns out, a necessary condition is that these data, together with the knowledge about the physical set-up of sender and receiver, allow to establish a proof of effective entanglement between the two parties. We then demonstrate methods to systematically search for such a proof in basic settings, involving the 2-, 4-, and 6-state protocols.