High-dimensional quantum systems offer a number of advantages in larger information capacity, stronger noise resiliency, higher improved efficiency and accuracy over the qubit systems. In quantum communication the maximally entangled states will inevitably become mixed states or less-entangled pure states by the channel noise during the practical transmission or storage. We propose a universal scheme to concentrate nonlocal high-dimensional generalized Bell states with unknown parameters. After the cross-Kerr nonlinearities,
X-quadrature homodyne measurements, and single-partite projection measurements are performed only at Bob's site, a two-qutrit maximally entangled Bell state can be distilled, while previous entanglement concentration protocols (ECPs) mostly focused on two-level qubit systems. The concentrated partially entangled qubit states, reserved as the by-product are the fascinating resources for some quantum information processing tasks. Moreover, single-qutrit projection measurement, the key ingredient for our ECP with unknown parameters, are completed by using linear optical elements. Additionally, linear optical high-dimensional ECP with known parameters are also designed.
The entanglement concentration processes for unknown and known non-maximally spin-entangled states are investigated with the aid of intraparticle path–spin hybrid entanglement based on quantum entanglement swapping. The results indicate that the maximally entangled state can be gained with a certain probability by applying operations at local region and classical communication. There is no collective measurement at the end of the realization process, which makes our schemes more efficient to administer.
Entanglement is one of the most useful resources in quantum information processing. If a sender and receiver share noiseless entanglement in the form of maximally entangled states, then Chapter 6 showed how they can teleport quantum bits between each other with the help of classical communication, or they can double the capacity of a noiseless qubit channel for transmitting classical information. We will see further applications in Chapter 20 where they can exploit noiseless entanglement to assist in the transmission of classical or quantum data over a noisy quantum channel. Given the utility of maximal entanglement, a reasonable question is to ask what a sender and receiver can accomplish if they share pure entangled states that are not maximally entangled. In the quantum Shannon-theoretic setting, we make the further assumption that the sender and receiver can share many copies of these pure entangled states. We find out in this chapter that they can “concentrate” these non-maximally entangled states to maximally entangled ebits, and the optimal rate at which they can do so in the asymptotic limit is equal to the “entropy of entanglement” (the von Neumann entropy of half of one copy of the original state). Entanglement concentration is thus another fundamental task in noiseless quantum Shannon theory, and it gives a different operational interpretation to the von Neumann entropy. Entanglement concentration is perhaps complementary to Schumacher compression in the sense that it gives a firm quantum information-theoretic interpretation of the term “ebit” (just as Schumacher compression did for the term “qubit”), and it plays a part in demonstrating how the entropy of entanglement is the unique measure of entanglement for pure bipartite states.
Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, in practice, it is difficult to distribute quantum entanglement over a long distance, due to the absorption and noise in quantum channels. A solution to this challenge is a quantum repeater, which can extend the distance of entanglement distribution. In this scheme, the time consumption of classical communication and local operations takes an important place with respect to time efficiency. Motivated by this observation, we consider a basic quantum repeater scheme that focuses on not only the optimal rate of entanglement concentration but also the complexity of local operations and classical communication. First, we consider the case where two different two-qubit pure states are initially distributed in the scenario. We construct a protocol with the optimal entanglement-concentration rate and less consumption of local operations and classical communication. We also find a criterion for the projective measurements to achieve the optimal probability of creating a maximally entangled state between the two ends. Second, we consider the case in which two general pure states are prepared and general measurements are allowed. We get an upper bound on the probability for a successful measurement operation to produce a maximally entangled state without any further local operations.
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.
Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.