Distillable entanglement under dually non-entangling operations

Area of Science:

• Quantum Information Theory
• Quantum Computing
• Entanglement Theory

Background:

• Calculating entanglement distillation rates from noisy quantum states is a long-standing challenge.
• Local operations and classical communication (LOCC) are typically considered for entanglement manipulation.

Purpose of the Study:

• To find an exact solution for entanglement distillation under dually non-entangling (DNE) operations.
• To explore the implications of DNE operations on entanglement distillation and dilution.

Main Methods:

• Introduced and analyzed dually non-entangling (DNE) operations, a relaxation of LOCC.
• Developed a modified regularised relative entropy of entanglement formula for DNE distillable entanglement.
• Constructed a general upper bound for DNE distillable entanglement.

Main Results:

• An exact formula for DNE distillable entanglement was derived, coinciding with a modified regularised relative entropy of entanglement.
• Entanglement can be distilled from any entangled state under DNE operations.
• Proved that separably measured relative entropy of entanglement can be strictly smaller than the regularized standard relative entropy of entanglement, solving an open problem.

Conclusions:

• The DNE distillable entanglement provides a new regularised formula, the second known for any free operations.
• The study demonstrates a strong form of irreversibility in entanglement theory under DNE operations, particularly for entanglement dilution.