An upper bound for the purity of absolutely positive partial transpose states

Quantum states that remain positive under partial transpose after any global unitary transformation are known as absolutely positive partial transpose (APPT) states. Researchers have established an upper bound for the purity of these states, shedding light on the relationship between APPT states and absolutely separable states. The set of absolutely separable states is a subset of APPT states, with the two being equivalent in qubit-qudit systems. This finding has implications for quantum computing and cryptography, as it refines understanding of quantum state properties¹. The identification of an upper bound for APPT state purity contributes to the development of quantum information theory, which underlies advancements in quantum computing and cryptography. So what matters to practitioners is that this research contributes to a deeper understanding of quantum states, ultimately informing the development of secure quantum communication protocols.