Auxiliary pure quantum entangled states shared between two parties can act as catalysts in bipartite entanglement transformations. The participation of a catalyst state in the transformation can enhance its success probability. We consider transformations involving entanglement concentration of a finite number of copies of arbitrary two-qubit pure states into a single copy of a maximally entangled two-qubit pure state using bipartite local quantum operations and classical communication aided by a catalyst state. We show the enhancement of success probabilities of the catalyst-assisted procedure compared to the case where no catalysts are used. The optimal two-qubit catalyst and the maximum probability of the transformation using such catalysts can be obtained analytically. The enhancement of concentration success probability using catalysts of higher dimensions is demonstrated numerically. Finally, catalyst aided strategies for obtaining multiple maximally entangled two-qubit states are discussed.
An optimal local conversion strategy between any two pure states of a bipartite system is presented. It is optimal in that the probability of success is the largest achievable if the parties which share the system, and which can communicate classically, are only allowed to act locally on it. The study of optimal local conversions sheds some light on the entanglement of a single copy of a pure state. We propose a quantification of such an entanglement by means of a finite minimal set of new measures from which the optimal probability of conversion follows.
We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement assisted local operations and classical communications using a two-qubit catalyst state. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. Entanglement assisted strategies for obtaining multiple Bell states are discussed.
Suppose two distant observers Alice and Bob share a pure bipartite quantum state. By applying local operations and communicating with each other using a classical channel, Alice and Bob can manipulate it into some other states. Previous investigations of entanglement manipulations have been largely limited to a small number of strategies and their average outcomes. Here we consider a general entanglement manipulation strategy, and go beyond the average property. For a pure entangled state shared between two separated persons Alice and Bob, we show that the mathematical interchange symmetry of the Schmidt decomposition can be promoted into a physical symmetry between the actions of Alice and Bob. Consequently, the most general (multistep two-way-communications) strategy of entanglement manipulation of a pure state is, in fact, equivalent to a strategy involving only a single (generalized) measurement by Alice followed by one-way communications of its result to Bob. We also prove that strategies with one-way communications are generally more powerful than those without communications. In summary, one-way communications is necessary and sufficient for entanglement manipulations of a pure bipartite state. The supremum probability of obtaining a maximally entangled state (of any dimension) from an arbitrary state is determined, and a strategy for achieving this probability is constructed explicitly. One important question is whether collective manipulations in quantum mechanics can greatly enhance the probability of large deviations from the average behavior. We answer this question in the negative by showing that, given n pairs of identical partly entangled pure states $(|\ensuremath{\Psi}〉)$ with entropy of entanglement $E(|\ensuremath{\Psi}〉),$ the probability of getting
nK $[K>E(|\ensuremath{\Psi}〉)]$ singlets out of entanglement concentration tends to zero as n tends to infinity.
Considering pure quantum states, entanglement concentration is the procedure where from
N copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for
N=1. However, the associated success probability can be extremely low while increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for
N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function
Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of
Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.
copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.