The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial time scaling of subsystem (or partial Planck's constant scaling) which was used to formulate recently separability criterion for continous variables.A measure of entanglement which is a generalization of negativity measure is introduced being based on tomographic probability description of spin states.The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial time scaling of subsystem (or partial Planck's constant scaling) which was used to formulate recently separability criterion for continous variables.A measure of entanglement which is a generalization of negativity measure is introduced being based on tomographic probability description of spin states.

arXiv:quant-ph/0509006Journal of Physics A Mathematical and GeneralNov 16, 200514 citations

Truncated moment sequences and a solution to the channel separability problem

Nadia Milazzo, Daniel Braun, O. Giraud

We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamio\l{}kowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae, and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$ . This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix ${M}_{t}(y)$ of order $t$ . We exploit the algorithm to numerically investigate separability of families of two-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$ , a criterion which remains inconclusive for Choi matrices with $N=0$ .We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamio\l{}kowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae, and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix ${M}_{t}(y)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of two-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.

arXiv:2006.15003Physical Review ANov 6, 20205 citations

Generalized Probability-Changing Algorithm

Yusuke Tomita, Yutaka Okabe

Springer proceedings in physicsJan 1, 20041 citation

Deciding separability with a fixed error

David Pérez-Garcı́a

arXiv:quant-ph/0407247Physics Letters AAug 17, 200411 citations

Quantum extension of conditional probability

Nicolas J. Cerf, Christoph Adami

We analyze properties of the quantum conditional amplitude operator [Phys. Rev. Lett. 79, 5194 (1997)], which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More specifically, it is proven that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. A related separability criterion based on the non-negativity of the von Neumann conditional entropy is also exhibited.We analyze properties of the quantum conditional amplitude operator [Phys. Rev. Lett. 79, 5194 (1997)], which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More specifically, it is proven that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. A related separability criterion based on the non-negativity of the von Neumann conditional entropy is also exhibited.

arXiv:quant-ph/9710001Physical Review AAug 1, 1999135 citations

y

. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables

n

in the tms and on the size of the moment matrix

{M}_{t}(y)

of order

t

. We exploit the algorithm to numerically investigate separability of families of two-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity

N

, a criterion which remains inconclusive for Choi matrices with

N=0