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Broadcasting and Quantumness in Quantum Information TheoryAuthor: Rounak Mundra Date: 2020-06-15 Report no: IIIT/TH/2020/46 Advisor:Indranil Chakrabarty AbstractQuantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operations. In this thesis, broadcasting of quantum resources beyond 2 ⊗ 2 systems is investigated. In particular, in 2 ⊗ 3 dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit (3 ⊗ 3) entangled pair with positive partial transpose on one of the local sides; and an absolutely separable qubit (2 ⊗ 2) pair on the other side of the input bipartite 2 ⊗ 3 dimensional resource state. Moving beyond entanglement, in 2 ⊗ d dimension, the impossibility to optimally broadcast quantum discord and quantum coherence (l1 -norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of discord and coherence are still possible. In the later part of the thesis, we propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is inconsequential, hence probability distribution of outcomes of any observable remains undisturbed. We define relative entropy of the two marginal probability distributions as a measure of quantumness in the state, which is revealed only in presence of two non-commuting observables. Like all other measures, we show that the proposed measure satisfies some basic axioms. Also, we find that this measure depicts complementarity with quantum coherence. The relation is more vivid when we choose one of the observables in such a way that its eigen basis matches with the basis in which the coherence is measured. Our result indicates that the quantumness in a single system is still an interesting question to explore and there can be an inherent feature of the state which manifests beyond the idea of quantum coherence. Full thesis: pdf Centre for Security, Theory and Algorithms |
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