We study the problem of extracting EPR pairs from a general source of entanglement. Suppose Alice and Bob share a bipartite state R which is reasonably to perfect EPR pairs. The only information Alice and Bob possess is a lower bound on the fidelity of R and a maximally entangled state. They wish to purify R using local operations and classical communication and output a state that is arbitrarily close to EPR pairs. We prove that on average, Alice and Bob cannot increase the fidelity of the input state significantly. On the other hand, there exist that may fail with a small probability, and otherwise will output states arbitrarily close to EPR pairs with very high probability. These come from the purity-testing protocols of Barnum et al.
We study the problem of extracting EPR pairs from a general source of entanglement. Suppose Alice and Bob share a bipartite state R which is reasonably to perfect EPR pairs. The only information Alice and Bob possess is a lower bound on the fidelity of R and a maximally entangled state. They wish to purify R using local operations and classical communication and output a state that is arbitrarily close to EPR pairs. We prove that on average, Alice and Bob cannot increase the fidelity of the input state significantly. On the other hand, there exist that may fail with a small probability, and otherwise will output states arbitrarily close to EPR pairs with very high probability. These come from the purity-testing protocols of Barnum et al.
We study the problem of extracting Einstein-Podolsky-Rosen (EPR) pairs from a general source of entanglement. Suppose Alice and Bob share a bipartite state /spl rho/ which is "reasonably close" to perfect EPR pairs. The only information Alice and Bob possess is a lower bound on the fidelity of /spl rho/ and a maximally entangled state. They wish to "purify" /spl rho/ using local operations and classical communication, and output a state that is arbitrarily close to EPR pairs. We prove that, on average, Alice and Bob cannot increase the fidelity of the input state significantly. On the other hand, there exist protocols that may fail with a small probability, and otherwise will output states arbitrarily close to EPR pairs with very high probability. These protocols come from the "purity-testing protocols" of H. Barnum et al. (2001).
Suppose Alice and Bob jointly possess a pure state, $|\ensuremath{\psi}〉$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|\ensuremath{\psi}〉$ into another joint state $|\ensuremath{\varphi}〉$. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems.
In quantum information science, it is often the question what distantly located parties sharing EPR pairs can achieve if they are restricted to only local operations and classical communication (LOCC). State preparation and transformation is one of such tasks, which have been attracted considerable interest since the early years of the field. It is well-known that starting with EPR pairs, any two-qubit pure state can be prepared via only LOCC. Thus EPR pairs form a universal resource. However, the situation is very different when the multipartite entanglement is considered, because in multipartite entanglement, there are distinct classes of entanglement, which cannot be converted into each other with unit fidelity even under stochastic local operation and classical communication (SLOCC), e.g., two distinct classes of states, GHZ-type and W-type states for the tripartite cases [1]. There exists no tripartite state that can be used as a universal resource to generate arbitrary tripartite pure states using SLOCC. For this purpose, one must look for a resource in larger systems such as many shared EPR pairs to extract the desired multipartite state. For example, there is a direct way of converting two EPR pairs into a three-qubit GHZ-type state [2], which then can be used to prepare approximate W state [3]. In this conversion from GHZ to W state, there is a trade-off between the fidelity and success probability. Unit fidelity cannot be achieved with non-zero probability, which confirms that GHZ- and W-type states belong to distinct classes.
In order to perform faithfully quantum communication protocols such as quantum teleportation, superdense coding, quantum key distribution, and quantum secret sharing, we need the entanglement purification process to make a maximal entanglement out of many copies of the partially entangled pairs by using local operations and classical communication. In this dissertation,\nwe analyze the efficiency of several entanglement purification protocols for qubit states and qudit states, and present a new efficient entanglement purification protocol. Furthermore, we show that our method can be applied to the existing best protocol\nso as to improve the efficiency.
States of sufficiently low purity are separable and cannot be entangled by unital (purity-non-generating) operations. Since high-purity states are experimentally demanding, it is natural to ask how much purity a state must possess to enable entanglement generation. Absolutely separable states remain separable under all deterministic unital channels, and so cannot deterministically generate entanglement in this setting. We show, however, that some absolutely separable states can generate entanglement via probabilistic protocols that do not produce purity. This motivates the study of states that fail to generate entanglement with any non-zero probability, which we call completely absolutely separable; we give a full characterization of this class. Along the way, we derive a novel sufficient condition for separability that depends only on the largest and smallest eigenvalues, along with the smallest local dimension and is independent of all previously known spectral separability criteria.
Quantum entanglement distillation protocols are LOCC protocols between Alice and Bob that convert imperfect EPR pairs, or, in general, partially entangled bipartite states into perfect or near-perfect EPR pairs. The classical communication complexity of these protocols is the minimal amount of classical communication needed for the conversion. In this paper, we focus on the communication complexity of protocols that operate with incomplete information, i.e., where the inputs are mixed states and/or prepared adversarially. We study 3 models of imperfect EPR pairs. In the measure-r model, r out of n EPR pairs are measured by an adversary; in the depolarization model, Bob's share of qubits underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the measure-r model and the depolarization model, we prove tight and almost-tight bounds on the outcome of LOCC protocols that don't use communication. For the fidelity model, we prove a lower bound on the communication complexity that matches the upper bound given by Ambainis, Smith, and Yang [ASY02].