Almost qudits in the prepare-and-measure scenario

Abstract

Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we introduce and investigate quantum information encoded in carriers that nearly, but not entirely, correspond to standard qudits. We demonstrate the relevance of this concept for semi-device-independent quantum information by showing how small higher-dimensional components can significantly compromise the conclusions of established protocols. Then we provide a general method, based on semidefinite relaxations, for bounding the set of almost qudit correlations, and apply it to remedy the demonstrated issues. This method also offers a novel systematic approach to the well-known task of device-independent tests of classical and quantum dimensions with unentangled devices. Finally, we also consider viewing almost qubit systems as a physical resource available to the experimenter and determine the optimal quantum protocol for the well-known Random Access Code.

5 + 5 pages, 6 figures. Changelog: v2 minor correction

References in corpus (12)

• Secure device-independent quantum key distribution with causally independent measurement devices
• A universal qudit quantum processor with trapped ions
• The Communication Cost of Simulating Bell Correlations
• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• Semi-device-independent security of one-way quantum key distribution
• Quantum Random Access Codes using Single $d$-level Systems
• Bounding the set of finite dimensional quantum correlations
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Semi-device-independent framework based on restricted distrust in prepare-and-measure experiments
• Properties of dimension witnesses and their semi-definite programming relaxations
• Experimental semi-device-independent certification of entangled measurements

Cited by in corpus (16)

• Semidefinite programming relaxations for quantum correlations
• Scalable entanglement certification via quantum communication
• Quantum stochastic communication via high-dimensional entanglement
• Prepare-and-measure scenarios with photon-number constraints
• Information capacity of quantum communication under natural physical assumptions
• Bound entangled states are useful in prepare-and-measure scenarios
• Simple and general bounds on quantum random access codes
• Imprecision plateaus in quantum steering
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Compression of Entanglement Improves Quantum Communication
• The role of entanglement in energy-restricted communication and randomness generation
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Random access codes via quantum contextual redundancy
• Semi-device-independent self-testing of unitary operations
• Uncertainty-disturbance relations and applications
• Semi-device-independent certification of high-dimensional quantum channels