Some aspects of the interplay between bipartite correlations and quantum channels

Abstract

This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii) the robustness of non-Gaussian entanglement under symmetric local noisy attenuator and amplifier channels, and finally, (iv) the connection between nonclassicality breaking and entanglement breaking for single-mode bosonic Gaussian channels.

arXiv commentPhD Thesis (defended Jan 2014), 233p, The Institute of Mathematical Sciences. The thesis is based on arXiv:1103.1311, arXiv:1304.4857, arXiv:1306.5536, arXiv:1311.0210, with background material from arXiv:1012.4266 ([quant-ph])

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• Quantum Capacities of Bosonic Channels
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• Operator-sum Representation for Bosonic Gaussian Channels
• Quantum discord and local demons
• Observable measure of bipartite quantum correlations
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• Continuity bounds for entanglement
• Degradability of Bosonic Gaussian channels
• Witnessing quantum discord in 2 x N systems
• On Random Unitary Channels
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• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
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• Entanglement, discord and the power of quantum computation
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• Quantifying quantum discord and entanglement of formation via unified purifications
• Quantum control and the Strocchi map
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• The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel
• Entanglement of Formation for a Class of Quantum States
• Quantum linear amplifier enhanced by photon subtraction and addition
• Maps for general open quantum systems and a theory of linear quantum error correction
• On the optimal feedback control of linear quantum systems in the presence of thermal noise
• Continuous variable entanglement distillation of Non-Gaussian Mixed States
• Wigner-function theory and decoherence of the quantum-injected optical parametric amplifier
• Entanglement and nonclassicality for multi-mode radiation field states
• A new criteria for zero quantum discord
• Optimized design of universal two-qubit gates
• Robust two-qubit quantum registers
• Entanglement distillation for continuous-variables under a thermal environment: Effectiveness of a non-Gaussian operation
• The optimal unitary dilation for bosonic Gaussian channels
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• Local witness for bipartite quantum discord
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• A Condition for the Nullity of Quantum Discord
• Linear amplification and quantum cloning for non-Gaussian continuous variables
• Discording power of quantum evolutions
• Entanglement Cost of Three-Level Antisymmetric States
• Probabilistic Quantum Control Via Indirect Measurement
• How much quantum noise of amplifiers is detrimental to entanglement
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• The most robust entangled state of light
• Hamiltonian Composite Dynamics Can Almost Always Lead To Negative Reduced Dynamics
• Quantum discord plays no distinguished role in characterization of complete positivity: Robustness of the traditional scheme
• Entanglement of Formation for Gaussian States
• Quantum discord for two-qubit $X$-states: A comprehensive approach inspired by classical polarization optics
• Encoding a qubit into multilevel subspaces