The positive partial transpose conjecture for n=3

Abstract

We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the proof found Müller-Hermes. Müller-Hermes announced that this conjecture is true for the states on ${\mathbb{C}}_3\otimes {\mathbb{C}}_3$ \cite{hermes} recently. The PPT square conjecture in the case $n\ge 4$ is still open.

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• Symmetric quantum states: a review of recent progress
• Random covariant quantum channels
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• The detection power of real entanglement witnesses under local unitary equivalence
• Detection of genuine tripartite entanglement by two bipartite entangled states
• $k$-Positive Maps: New Characterizations and a Generation Method
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Entanglement Superactivation in Multiphoton Distillation Networks