LOCC indistinguishable orthogonal product quantum states.

Area of Science:

• Quantum Information Theory
• Quantum Many-Body Systems
• Quantum Foundations

Background:

• Local operations and classical communication (LOCC) are fundamental constraints in quantum information processing.
• Distinguishing quantum states is crucial for quantum communication and computation.
• Quantum nonlocality without entanglement is a key phenomenon in understanding quantum correlations.

Purpose of the Study:

• To construct novel families of orthogonal product quantum states.
• To investigate the distinguishability of these states under LOCC.
• To provide a generalized framework for constructing and analyzing such states.

Main Methods:

• Construction of two families of orthogonal product quantum states in (2k+i)⊗(2l+j) and (3k+i)⊗(3l+j) systems.
• Analysis of the tiling structure and extendibility of these quantum states.
• Calculation of non-commutativity to quantify quantumness and assess local indistinguishability.

Main Results:

• Successfully constructed two families of quantum product states that are indistinguishable by LOCC.
• Demonstrated that the first family is unextendible, while the second is extendible.
• Developed a general method for judging the indistinguishability of orthogonal product states.

Conclusions:

• The constructed states provide new examples of quantum nonlocality without entanglement.
• The generalized construction in (3k+i)⊗(3l+j) systems unifies and extends previous works.
• This research complements existing understanding of quantum correlations and state distinguishability.