In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD does not happen only when all maps of the family are induced by local unitary operations. We prove that is the case for dynamics where all maps are induced by unitaries and, for pairs of qubits, where all maps are unital. Moreover, we prove some results about unitaries/CPTP maps preserving product/pure states.In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD does not happen only when all maps of the family are induced by local unitary operations. We prove that is the case for dynamics where all maps are induced by unitaries and, for pairs of qubits, where all maps are unital. Moreover, we prove some results about unitaries/CPTP maps preserving product/pure states.

arXiv:1510.06466Oct 22, 20150 citations

Local cloning of multipartite entangled states

Guruprasad Kar, Ramij Rahaman

Quantum Information ProcessingAug 31, 20117 citations

Smallest disentangling state spaces for general entangled bipartite quantum states

Hussain Anwar, Jevtic, Sania, Rudolph, Oliver +1 more

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].

arXiv:1511.03196Nov 10, 20150 citations

Entanglement in Bipartite Quantum States

Ved Prakash Gupta, Prabha Mandayam, Viakalathur Shankar Sunder

Lecture notes in physicsJan 1, 20150 citations

Local cloning of entangled states

Vlad Gheorghiu, Li Zhi Yu, Scott M. Cohen

We investigate the conditions under which a set $\mathcal{S}$ of pure bipartite quantum states on a $D\ifmmode\times\else\texttimes\fi{}D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in $\mathcal{S}$ must be full Schmidt rank and equally entangled under the $G$ -concurrence measure, and (ii) the set $\mathcal{S}$ can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$ , the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$ ; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary ``shift'' operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in $D=3$ we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in $\mathcal{S}$ . All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.We investigate the conditions under which a set $\mathcal{S}$ of pure bipartite quantum states on a $D\ifmmode\times\else\texttimes\fi{}D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in $\mathcal{S}$ must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set $\mathcal{S}$ can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary ``shift'' operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in $D=3$ we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in $\mathcal{S}$. All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.

arXiv:1004.5126Physical Review AAug 11, 201011 citations

Local cloning of arbitrarily entangled multipartite states (4 pages)

Marie Ericsson, Alastair Kay

Physical Review AJan 1, 20062 citations

We investigate the conditions under which a set

\mathcal{S}

of pure bipartite quantum states on a $D\ifmmode\times\else\texttimes\fi{}D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in

\mathcal{S}

must be full Schmidt rank and equally entangled under the

G

-concurrence measure, and (ii) the set

\mathcal{S}

can be extended to a larger clonable set generated by a finite group

G

of order

|G|=N

, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides

D

exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all

D

; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary ``shift'' operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in

D=3

we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in

\mathcal{S}

. All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.