Communication of partial ignorance with qubits

Abstract

We introduce a class of communication tests where the task is to communicate partial ignorance by means of a physical system. We present a full characterization of the implementations of these tests in the qubit case and partial results for qudits. A peculiar observation is that two physical systems with the same operational dimensions may differ with respect to implementations of these tasks, as is shown to be the case for the qubit and rebit. Finally, we consider the natural question whether some of the communication tests are more difficult than others. A new preordering that we call the ultraweak matrix majorization is presented to answer this question in a theory-independent way.

arXiv commentminor corrections in v2

References in corpus (11)

• Symmetric Informationally Complete Quantum Measurements
• On the reality of the quantum state
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• A derivation of quantum theory from physical requirements
• Constructing exact symmetric informationally complete measurements from numerical solutions
• Conditions for compatibility of quantum state assignments
• Conclusive Exclusion of Quantum States
• Positive semidefinite rank
• Distinguishability Measures and Entropies for General Probabilistic Theories
• Antidistinguishability of Pure Quantum States
• POVMs are equivalent to projections for perfect state exclusion of three pure states in three dimensions

Cited by in corpus (16)

• Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation
• The Communication Value of a Quantum Channel
• Simple Communication Complexity Separation from Quantum State Antidistinguishability
• Simple Information Processing Tasks with Unbounded Quantum Advantage
• Communication tasks in operational theories
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Unambiguous quantum state elimination for qubit sequences
• Certifying the Classical Simulation Cost of a Quantum Channel
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination
• Dispensing of quantum information beyond no-broadcasting theorem -- is it possible to broadcast anything genuinely quantum?
• Maximal Elements of Quantum Communication
• Partial ignorance communication tasks in quantum theory
• Can a qudit carry more information than a dit?
• How contextuality and antidistinguishability are related
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication