Proving the distillability problem of two-copy $$4\times 4$$ Werner states for monomial matrices

Chen, Lin; He, Huixia; Shi, Xian; Zhao, Lei

doi:10.1007/s11128-021-03098-w

Cited by 5 publications

(4 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, Wien discovered the radiation energy formula. Einstein recognized Planck's significance in physic disciplines at the close of the 19 th century and reestablished new hypotheses [1][2][3][4][5][6][7][8][9][10]. He believed that the quantum was unbroken and inseparable.…”

Section: The History Of Quantum Physicsmentioning

confidence: 99%

“…M physicists in the 19 th century believed that the atom was the smallest undivided unit. The original theory was proposed by Perrin, who believed that the atom was surrounded by charged particles, with electrons on the exterior [1][2][3][4][5][6][7][8][9][10]. Thomson imagined charged particles encircled by an electron ring.…”

Section: The History Of Quantum Physicsmentioning

confidence: 99%

“…Thomson imagined charged particles encircled by an electron ring. Later, Marsden conducted experiments disproving Thomson's idea [1][2][3][4][5][6][7][8][9][10]. Finally, Bohr demonstrated that only electrons emitted or absorbed energy during the transition and demonstrated that atoms are stable.…”

Section: The History Of Quantum Physicsmentioning

confidence: 99%

See 2 more Smart Citations

Distillability Problem of 4×4 Monomial Matrices

Wang

Zhang

2022

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

It is a fundamental problem in quantum information whether a particular quantum state of a composite system is entangled. It has enormous potential in quantum error correction, quantum cryptography, and quantum teleportation applications. This problem can be transferred in the form of a mathematical conjecture called the distillation conjecture. In the first section of this paper, relevant physical and mathematical information is presented, including basic linear algebra knowledge, the statement, and concrete applications of multiple mathematical knowledge like conjugate, eigenvalue, and singular value. Then, we introduce the distillation conjecture in a mathematical version for a more precise mathematical analysis. In an effort to make more significant headway in proving the conjecture, we selected some theories and findings relating to the Kronecker product, Kronecker sum, eigenvalue, and singular value, then evaluated and grouped them. In addition, we provided multiple proofs of the conjecture under varying conditions and made numerous attempts and hypotheses regarding how to establish the conjecture.

show abstract

Section: The History Of Quantum Physicsmentioning

confidence: 99%

Section: The History Of Quantum Physicsmentioning

confidence: 99%

See 1 more Smart Citation

Distillability Problem of 4×4 Monomial Matrices

Wang

Zhang

2022

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…Indeed, it is straightforward to check that ρ 2{n is not PPT and that it is (1-copy) undistillable. However, even proving the simplest case of 2-copy undistillability of this state when n " 4 remains elusive, despite significant effort [7,27].…”

mentioning

confidence: 99%

Birkhoff-James orthogonality in the trace norm, with applications to quantum resource theories

Johnston

Moein

Pereira

et al. 2022

ELA

View full text Add to dashboard Cite

Numerous results are presented that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set of positive semidefinite matrices. For example, a simple-to-test criterion that determines which Hermitian matrices are Birkhoff-James orthogonal, in the trace norm, to the set of all positive semidefinite diagonal matrices is developed. Applications in the theory of quantum resources are explored. For example, the quantum states that have modified trace distance of coherence equal to $1$ (the maximal possible value) are characterized, and a connection between the modified trace distance of $2$-entanglement and the NPPT bound entanglement problem is established.

show abstract

On the distillability problem of two-copy $$4\times 4$$ Werner states: matrices A, B of at most four nonzero entries

Chen

Feng

2023

Quantum Inf Process

View full text Add to dashboard Cite

Proving the distillability problem of two-copy $$4\times 4$$ Werner states for monomial matrices

Cited by 5 publications

References 22 publications

Distillability Problem of 4×4 Monomial Matrices

Distillability Problem of 4×4 Monomial Matrices

Birkhoff-James orthogonality in the trace norm, with applications to quantum resource theories

On the distillability problem of two-copy $$4\times 4$$ Werner states: matrices A, B of at most four nonzero entries

Contact Info

Product

Resources

About