Non-existence of invariant EPR correlation for two qudits, d>2

TL;DR

This paper proves that invariant perfect EPR correlations, present in two-qubit singlet states, do not exist in higher-dimensional bipartite states ($d extgreater 2$), impacting their use in long-distance quantum communication.

Contribution

The paper demonstrates the non-existence of invariant perfect EPR correlations in bipartite states with dimension $d extgreater 2$, highlighting a fundamental difference from qubit singlets.

Findings

Two-qubit singlet states have invariant perfect EPR correlations.

No such invariant correlations exist for $d extgreater 2$ bipartite states.

Implication: qubits are better suited for long-distance quantum communication.

Abstract

The two qubit (spin 1/2) singlet state has invariant perfect EPR correlations: if two observers measure {\em any} identical observables the results are always perfectly (anti-)correlated. We show that no such correlations exists in $d\otimes d$ pure or mixed bipartite quantum states if $d\geq3$. This points that two qubit singlets are high-quality quantum information carriers in long distance transmission: their correlations are unaffected by identical random unitary transformations of both qubits. Pairs of entangled qu$d$its, $d>2$, do not have this property. Thus, qu$d$it properties should be rather exploited only in protocols in which transmission is not a long distance one.