Quantum entanglement autodistillation in baryon pair decays

We study the spin-entangled mixed state of a spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math> baryon–antibaryon pair produced in the process <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>e</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>e</c:mi><c:mo>−</c:mo></c:msup><c:mo stretchy="false">→</c:mo><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi><c:mo>,</c:mo><c:msup><c:mi>ψ</c:mi><c:mo>′</c:mo></c:msup><c:mo stretchy="false">→</c:mo><c:mi mathvariant="script">B</c:mi><c:mover accent="true"><c:mi mathvariant="script">B</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math>. We show that the spin entanglement of the system can increase following the decays <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi mathvariant="script">B</k:mi><k:mo stretchy="false">→</k:mo><k:mi mathvariant="script">b</k:mi><k:mo>+</k:mo><k:mi>M</k:mi></k:mrow></k:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mover accent="true"><p:mi mathvariant="script">B</p:mi><p:mo stretchy="false">¯</p:mo></p:mover><p:mo stretchy="false">→</p:mo><p:mover accent="true"><p:mi mathvariant="script">b</p:mi><p:mo stretchy="false">¯</p:mo></p:mover><p:mo>+</p:mo><p:mover accent="true"><p:mi>M</p:mi><p:mo stretchy="false">¯</p:mo></p:mover></p:math>, where <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="script">b</ab:mi><ab:mo>,</ab:mo><ab:mover accent="true"><ab:mi mathvariant="script">b</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover></ab:math> are spin-<gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mrow><gb:mn>1</gb:mn><gb:mo>/</gb:mo><gb:mn>2</gb:mn></gb:mrow></gb:math> baryons and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>M</ib:mi><ib:mo>,</ib:mo><ib:mover accent="true"><ib:mi>M</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover></ib:math> are spin-0 mesons. This phenomenon, known as entanglement autodistillation, manifests as a probabilistic amplification of entanglement during the decay process. We analyze the underlying mechanism and show that this phenomenon depends only on the initial state of the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi mathvariant="script">B</mb:mi><mb:mover accent="true"><mb:mi mathvariant="script">B</mb:mi><mb:mo stretchy="false">¯</mb:mo></mb:mover></mb:math> system and the decay parameter <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msub><sb:mi>α</sb:mi><sb:mi>D</sb:mi></sb:msub></sb:math>, but not on the decay parameter <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msub><ub:mi>ϕ</ub:mi><ub:mi>D</ub:mi></ub:msub></ub:math>. This effect only arises when parity is violated in the decay, when <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>α</wb:mi><wb:mi>D</wb:mi></wb:msub><wb:mo>≠</wb:mo><wb:mn>0</wb:mn></wb:math>.