A Derivation of the Entangled State Representation by the Slice Theorem of the Wigner Operator

Key Points

• The central aim is to derive the entangled state representations using the Wigner operator and its properties.
• Utilized integration within the ordered product of operators for deducing the normal ordering form.
• Applied Weyl ordering concepts to describe the Wigner operator.
• Proposed the slice theorem to project a new pure-state density operator.
• Illustrated derivation of bi- and tri-partite entangled state representations.
• Successfully deduced the normal ordering and Weyl ordering forms of the Wigner operator.
• Proposed a new pure-state density operator that links classical and quantum tomography.
• Completed the derivation of both bi-partite and tri-partite entangled state representations.