IIIT Hyderabad Publications |
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Towards Detection and a Resource-Theoretic Characterization of Negative Quantum Conditional EntropyAuthor: Mahathi Vempati Date: 2021-11-26 Report no: IIIT/TH/2021/119 Advisor:Indranil Chakrabarty AbstractQuantum states that possess negative conditional von Neumann entropy (quantum conditional entropy) provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. This thesis deals with the characterization, study and detection of these resourceful states. The first part of the thesis deals with the detection of negative conditional entropy states. We characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of the methods proposed in the detection of useful states in several protocols. In the second part of the thesis, we introduce the resource-theory framework, and give pertinent directions for the study of conditional entropy under the resource-theoretic framework. Full thesis: pdf Centre for Security, Theory and Algorithms |
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