Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions

Abstract

We establish a mapping between a continuous variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system of arbitrary dimension. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite dimensional Hilbert space and thus can be considered as a universal resource of entanglement. As an explicit example of the formalism a two-mode CV entangled state is mapped onto a two-qutrit entangled state.

4 pages, 1 figure, revised version, an example added

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• Experimental Violation of Bell's Inequality in Spatial-Parity Space
• Bell's Inequalities for Continuous-Variable Systems in Generic Squeezed States
• What is "system": the information-theoretic arguments
• Synthesis and Analysis of Entangled Photonic Qubits in Spatial-Parity Space
• D-outcome measurement for a nonlocality test
• Test of nonlocality for a continuos-variable state based on arbitrary number of measurement outcomes
• Suitability of the approximate superposition of squeezed coherent states for various quantum protocols
• Multi-Component Bell Inequality and its Violation for Continuous Variable Systems
• Entanglement of mixed macroscopic superpositions: an entangling-power study
• Countinuous Quantum Hidden Subgroup Algorithms
• Bell violation for unknown continuous-variable states
• Quantum nonlocality for entanglement of quasiclassical states
• Correspondence between maximally entangled states in discrete and Gaussian regimes
• The role of degeneracy in the analogy between continuous variable and spin 1/2 systems
• Arbitrarily large violations of non-contextuality in single mode photon states with positive Wigner function