Investigation of the PPT Squared Conjecture for High Dimensions
Ryan Jin
TL;DR
This paper explores the PPT Squared Conjecture in high-dimensional quantum systems, introducing new methods to find counterexamples and advancing understanding of quantum channel properties.
Contribution
It proposes two novel approaches—decomposition and composition of quantum channels—and offers schemes for identifying potential counterexamples in higher dimensions.
Findings
A scheme involving composition of PPT channels suggests possible counterexamples.
New approaches provide tools for testing the conjecture in complex quantum systems.
Advances understanding of PPT channel behavior in high-dimensional quantum information.
Abstract
We present the positive-partial-transpose squared conjecture introduced by M. Christandl at Banff International Research Station Workshop: Operator Structures in Quantum Information Theory (Banff International Research Station, Alberta, 2012). We investigate the conjecture in higher dimensions and offer two novel approaches (decomposition and composition of quantum channels) and correspondingly, several schemes for finding counterexamples to this conjecture. One of the schemes involving the composition of PPT quantum channels in unsolved dimensions yields a potential counterexample.
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Taxonomy
TopicsMatrix Theory and Algorithms · VLSI and FPGA Design Techniques · Structural Analysis and Optimization