Wigner tomography of two qubit states and quantum cryptography

Abstract

Tomography of the two qubit density matrix shared by Alice and Bob is an essential ingredient for guaranteeing an acceptable margin of confidentiality during the establishment of a secure fresh key through the Quantum Key Distribution (QKD) scheme. We show how the Singapore protocol for key distribution is optimal from this point of view, due to the fact that it is based on so called SIC POVM qubit tomography which allows the most accurate full tomographic reconstruction of an unknown density matrix on the basis of a restricted set of experimental data. We illustrate with the help of experimental data the deep connections that exist between SIC POVM tomography and discrete Wigner representations. We also emphasise the special role played by Bell states in this approach and propose a new protocol for Quantum Key Distribution during which a third party is able to concede or to deny A POSTERIORI to the authorized users the ability to build a fresh cryptographic key.

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Cited by in corpus (27)

• The SIC Question: History and State of Play
• Constructing exact symmetric informationally complete measurements from numerical solutions
• Experimental characterization of qutrits using SIC-POVMs
• Quantum State Tomography with Joint SIC POMs and Product SIC POMs
• Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• Super-symmetric informationally complete measurements
• SICs and Algebraic Number Theory
• Experimental certification of an informationally complete quantum measurement in a device-independent protocol
• Quantum tomography via equidistant states
• Probability representation of quantum dynamics using pseudostochastic maps
• Linear Dependencies in Weyl-Heisenberg Orbits
• Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters
• What are the minimal conditions required to define a SIC POVM?
• Direct state reconstruction with coupling-deformed pointer observables
• Operational quasiprobabilities for qudits
• Scalable estimation of pure multi-qubit states
• Systems of Imprimitivity for the Clifford Group
• Optical experiment to test negative probability in context of quantum-measurement selection
• Bayesian error regions in quantum estimation I: analytical reasonings
• On the geometry and invariants of qubits, quartits and octits
• Local quantum overlapping tomography
• Studies of symmetries that give special quantum states the "right to exist"
• Completeness Stability of Quantum Measurements
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Minimal orthonormal bases for pure quantum state estimation
• Adaptive tomography of qubits: Purity versus statistical fluctuations