How to calculate entanglement cost

Louisiana State University physicist Mark Wilde and Xin Wang of Baidu Research's mathematical formula, called κ entanglement or max-logarithmic negativity (upper left) makes it possible to effeciently calculate the cost of entanglement, which in itself is an entanglement measure, in the creation of a two-party quantum state. Credit: Mark Wilde, LSU

Louisiana State University researchers have solved a 20-year-old problem in quantum information theory on how to calculate entanglement cost—a way to measure entanglement—in a manner that’s efficiently computable, useful, and broadly applicable in several quantum research areas.

The scientists describe how allowing a slightly wider range of physical operations than what’s known as LOCC (Local Operations and Classical Communication)—which have boggled quantum scientists with difficult math for some time—makes it possible to characterize the exact entanglement cost of a given quantum state. Their work closes a longstanding investigation in entanglement theory that is known as the “PPT exact entanglement cost of a quantum state.”

The most basic unit of entanglement is known as a Bell state. You can think of it as the smallest possible molecule consisting of two entangled atoms (qubits, really) whose entanglement is absolute—implying, if you could peek at one of them, you would know beyond a doubt that the other one would be its twin, with the same characteristics.

Basic entanglement units or Bell states are also known as e-bits. Entanglement can be looked at in two different ways: either how many e-bits it would take to prepare a quantum state, or how many e-bits one could extract or “distill” from a complex entangled state. (

The paper has been published in Physical Review Letters.

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