We consider a non-contextual inequality in the sequential measurement scenario and derive the optimal quantum violation of it without assuming the dimension of the system. Since the measurement is dichotomic and the dimension of the quantum system is arbitrary, we formulate the concept of degeneracy-breaking (DB) measurement depending on how many projectors are being used in the sequential measurement. We demonstrate that by increasing the number of projectors involved in the sequential measurement (thereby making the measurement more degeneracy breaking) the quantum violation of non-contextual inequality can be enhanced and can even reach up to its algebraic maximum. We demonstrate that the optimal quantum violations for different number of projectors serves as a quantum dimension witness.We consider a non-contextual inequality in the sequential measurement scenario and derive the optimal quantum violation of it without assuming the dimension of the system. Since the measurement is dichotomic and the dimension of the quantum system is arbitrary, we formulate the concept of degeneracy-breaking (DB) measurement depending on how many projectors are being used in the sequential measurement. We demonstrate that by increasing the number of projectors involved in the sequential measurement (thereby making the measurement more degeneracy breaking) the quantum violation of non-contextual inequality can be enhanced and can even reach up to its algebraic maximum. We demonstrate that the optimal quantum violations for different number of projectors serves as a quantum dimension witness.

quant-pharXiv:2603.26102Mar 30, 20260 citations

Characterizing high-Schmidt-number witnesses in arbitrary-dimensional systems

Liang Xiong, Nung-Sing Sze

Physical Review AApr 13, 20260 citations

Genuinely Unextendible Product Bases from Maximum Distance Separable Codes

Mao-Sheng Li

The existence of genuinely unextendible product bases (GUPBs), incomplete orthogonal sets of fully product states whose orthogonal complements contain no product vector across any bipartition, has remained an open problem. Here we construct GUPBs for any number $N\geq3$ of parties using classical maximum distance separable (MDS) codes. The MDS property imposes a rigidity on the induced product tiling across every bipartition; combined with Fourier mode deletion and a stopper state, this rigidity enforces genuine unextendibility. Consequently, the orthogonal complement of each GUPB is a genuinely entangled subspace whose normalized projector is invariant under partial transposition across every bipartition, yielding an explicit family of multipartite bound entangled states. We further construct GME witnesses that detect these states even though no fully decomposable witness can do so. Moreover, the resulting indistinguishability persists under arbitrary finite tensor powers and measurements separable across any bipartition. These results establish a direct connection between error-correcting codes and multipartite entanglement and provide an algebraic route to certifying genuinely multipartite bound entanglement.The existence of genuinely unextendible product bases (GUPBs), incomplete orthogonal sets of fully product states whose orthogonal complements contain no product vector across any bipartition, has remained an open problem. Here we construct GUPBs for any number $N\geq3$ of parties using classical maximum distance separable (MDS) codes. The MDS property imposes a rigidity on the induced product tiling across every bipartition; combined with Fourier mode deletion and a stopper state, this rigidity enforces genuine unextendibility. Consequently, the orthogonal complement of each GUPB is a genuinely entangled subspace whose normalized projector is invariant under partial transposition across every bipartition, yielding an explicit family of multipartite bound entangled states. We further construct GME witnesses that detect these states even though no fully decomposable witness can do so. Moreover, the resulting indistinguishability persists under arbitrary finite tensor powers and measurements separable across any bipartition. These results establish a direct connection between error-correcting codes and multipartite entanglement and provide an algebraic route to certifying genuinely multipartite bound entanglement.

quant-pharXiv:2608.09504Aug 11, 20260 citations

Swapping and singlet projection as generic entanglement witnesses for quantum Heisenberg spin- $s$ systemsSwapping and singlet projection as generic entanglement witnesses for quantum Heisenberg spin-$s$ systems

Guang-Ming Zhang, Xiaoguang Wang

Based on the SU( $N$ ) representation of group theory, we derive the generalized SU( $N$ ) invariant swapping operator for the quantum Heisenberg spin- $s$ systems ( $N=2s+1$ ). It has been demonstrated that the partial transposition of the swapping operator is equal to the singlet pairing projection in the tensor product space of the fundamental SU( $N$ ) representation and its conjugate one. For general SU(2) invariant bipartite spin- $s$ systems, the expectation value of the swapping operator is found to be the leading term in the negativity expression with respect to the corresponding density matrix. Generalized to the many-body SU(2) invariant states, we prove that the expectation values of the swapping operator and the singlet pairing projector can be regarded as two generic entanglement witnesses, which can be detectable in future experiments.Based on the SU($N$) representation of group theory, we derive the generalized SU($N$) invariant swapping operator for the quantum Heisenberg spin-$s$ systems ($N=2s+1$). It has been demonstrated that the partial transposition of the swapping operator is equal to the singlet pairing projection in the tensor product space of the fundamental SU($N$) representation and its conjugate one. For general SU(2) invariant bipartite spin-$s$ systems, the expectation value of the swapping operator is found to be the leading term in the negativity expression with respect to the corresponding density matrix. Generalized to the many-body SU(2) invariant states, we prove that the expectation values of the swapping operator and the singlet pairing projector can be regarded as two generic entanglement witnesses, which can be detectable in future experiments.

Jan 19, 20060 citations

N\geq3

of parties using classical maximum distance separable (MDS) codes. The MDS property imposes a rigidity on the induced product tiling across every bipartition; combined with Fourier mode deletion and a stopper state, this rigidity enforces genuine unextendibility. Consequently, the orthogonal complement of each GUPB is a genuinely entangled subspace whose normalized projector is invariant under partial transposition across every bipartition, yielding an explicit family of multipartite bound entangled states. We further construct GME witnesses that detect these states even though no fully decomposable witness can do so. Moreover, the resulting indistinguishability persists under arbitrary finite tensor powers and measurements separable across any bipartition. These results establish a direct connection between error-correcting codes and multipartite entanglement and provide an algebraic route to certifying genuinely multipartite bound entanglement.

Swapping and singlet projection as generic entanglement witnesses for quantum Heisenberg spin-

s

systems

Based on the SU(

N

) representation of group theory, we derive the generalized SU(

N

) invariant swapping operator for the quantum Heisenberg spin-

s

systems (

N=2s+1

). It has been demonstrated that the partial transposition of the swapping operator is equal to the singlet pairing projection in the tensor product space of the fundamental SU(

N

) representation and its conjugate one. For general SU(2) invariant bipartite spin-

s

systems, the expectation value of the swapping operator is found to be the leading term in the negativity expression with respect to the corresponding density matrix. Generalized to the many-body SU(2) invariant states, we prove that the expectation values of the swapping operator and the singlet pairing projector can be regarded as two generic entanglement witnesses, which can be detectable in future experiments.