One of the many bizarre features of entanglement is that Alice, by sending a qubit to Bob in a separable state, can generate some entanglement between herself and Bob. This protocol is stripped down to the bare essentials to better elucidate the key properties of the initial resource state that enable this entanglement distribution. The necessary and sufficient conditions under which the correlations of a Bell-diagonal state serve as a useful resource are proven, giving upper and lower bounds on the entanglement that can be distributed when those conditions are met.
One of the many bizarre features of entanglement is that Alice, by sending a qubit to Bob in a separable state, can generate some entanglement between herself and Bob. This protocol is stripped down to the bare essentials to better elucidate the key properties of the initial resource state that enable this entanglement distribution. The necessary and sufficient conditions under which the correlations of a Bell-diagonal state serve as a useful resource are proven, giving upper and lower bounds on the entanglement that can be distributed when those conditions are met.
The main focus of this thesis is quantum entanglement and, more specifically, pro- tocols that allow its distribution between distant places. In the last decades, with the rise of attention on quantum technologies, entangle- ment is mostly seen as a resource, that could be exchanged, measured, and ideally stored and used when convenient. However, entanglement is not as stable and cheap as the classical resources. One reason for this is that entanglement between two quantum systems is easily disrupted by the interaction with the environment that surrounds them. The presence of noise is even more significant when we wish to entangle two systems that are very far away, a task that is essential for quantum communication technologies. In this case, what can disrupt the entanglement is not only the noise that the particles experience locally, but also the noise in the quantum channel during the communication process, which can be significant over long distances. For this reason, it is important to design distribution protocols that work well in such conditions. In 2003, Cubitt et al. showed the existence of a very curious class of protocols, often called entanglement distribution with separable states (EDSS). They proved that a non-entangled (separable) carrier can be used to increase, or even gener- ate entanglement between two already distant parties. From this, some questions arise. First, what limits or allows an entanglement distribution protocol, if not the entanglement that is sent. Quantum discord was shown to be a necessary, but not sufficient, resource for entanglement distribution. Another natural question is whether these protocols can beat others, for technological purposes, especially in noisy conditions. I will describe some work I have done in an attempt to partially 9 address both of these questions. After introducing various tools and concepts that are useful to understand this topic (chapter 1) and motivate the necessity of entanglement distribution in quantum communication (chapter 2), I will describe a proof-of-principle experiment demon- strating EDSS schemes (chapter 3). Later (chapter 4), I will introduce a more general classification of distribution protocols (excessive or non-excessive protocols), based on whether the entanglement gain is larger than the one that is communicated, describing specific examples and general properties of such protocols. I will then partially address the problem regarding the robustness to the noise of communica- tion protocols (chapter 5). Finally, in chapter 6, I will describe how entanglement of a bipartite state can grow with a quantum measurement with unknown results. I discuss the properties of the measurement and of the initial state that make this process effective.
We experimentally demonstrate a protocol for entanglement distribution by a separable quantum system. In our experiment, two spatially separated modes of an electromagnetic field get entangled by local operations, classical communication, and transmission of a correlated but separable mode between them. This highlights the utility of quantum correlations beyond entanglement for the establishment of a fundamental quantum information resource and verifies that its distribution by a dual classical and separable quantum communication is possible.
A user, Alice, wants to get server Bob to implement a quantum computation for her. However, she wants to leave him blind to what she's doing. What are the minimal communication resources Alice must use in order to achieve information-theoretic security? In this paper, we consider a single step of the protocol, where Alice conveys to Bob whether or not he should implement a specific gate. We use an entropy-bounding technique to quantify the minimum number of qubits that Alice must send so that Bob cannot learn anything about the gate being implemented. We provide a protocol that saturates this bound. In this optimal protocol, the states that Alice sends may be entangled. For Clifford gates, we prove that it is sufficient for Alice to send separable states.
In recent years, exploration of the possible use of separable states as a resource to achieve quantum information processing (QIP) tasks has been gaining increasing significance. In this context, a particularly important demonstration has been that nonvanishing discord is the necessary condition for separable states to be used as a resource for remotely preparing any arbitrary pure target state [Nat. Phys. 8, 666 (2012)]. The present work stems from our observation that not only can resource states with the same discord imply different efficiencies (in terms of average fidelity) of the remote state preparation (RSP) protocol, but also states with higher discord can imply lower RSP efficiency. Therefore, this necessitates identification of the relevant feature of quantum correlations that can appropriately quantify the effectiveness of the resource state for the RSP protocol. To this end, for the two-qubit Bell-diagonal states, we show that an appropriate measure of simultaneous correlations in three mutually unbiased bases can serve to quantify the usefulness of the resource for the RSP task using entangled as well as separable states, including nondiscordant states as a resource. In particular, it is revealed that zero-discord states with such a nonvanishing measure can be useful for remotely preparing a subset of pure target states. Thus, this work shows that, using separable states, an effective resource for QIP tasks such as RSP can be provided by simultaneous correlations in mutually unbiased bases.
A new scheme of Quantum Key Distribution is proposed using three entangled particles in a GHZ state. Alice holds a 3-particle source and sends two particles to Bob, keeping one with herself. Bob uses one particle to generate a secure key, and the other to generate a master-key. This scheme should prove to be harder to break in non-ideal situations as compared to the standard protocols BB84 and Eckert. The scheme uses the concept of Quantum Disentanglement Eraser. Extension to multi-partite scheme has also been investigated.