Deterministic transformations of three-qubit entangled pure states (original) (raw)

Local Deterministic Transformations of Three-Qubit Pure States

2001

The properties of deterministic LOCC transformations of three qubit pure states are studied. We show that the set of states in the GHZ class breaks into an infinite number of disjoint classes under this type of transformation. These classes are characterized by the value of a quantity that is invariant under these transformations, and is defined in terms of the coefficients of a particular canonical form in which only states in the GHZ class can be expressed. This invariant also imposes a strong constraint on any POVM that is part of a deterministic protocol. We also consider a transformation generated by a local 2-outcome POVM and study under what conditions it is deterministic, i.e., both outcomes belong to the same orbit. We prove that for real states it is always possible to find such a POVM and we discuss analytical and numerical evidence that suggests that this result also holds for complex states. We study the transformation generated in the space of orbits when one or more p...

Investigating three qubit entanglement with local measurements

In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators which can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.

Control and Measurement of Three-Qubit Entangled States

Science, 2004

We report the deterministic creation of maximally entangled three-qubit states-specifically the Greenberger-Horne-Zeilinger (GHZ) state and the W state-with a trapped-ion quantum computer. We read out one of the qubits selectively and show how GHZ and W states are affected by this local measurement. Additionally, we demonstrate conditional operations controlled by the results from reading out one qubit. Tripartite entanglement is deterministically transformed into bipartite entanglement by local operations only. These operations are the measurement of one qubit of a GHZ state in a rotated basis and, conditioned on this measurement result, the application of single-qubit rotations.

Classification of nonasymptotic bipartite pure-state entanglement transformations

Physical Review A, 2002

Let {|ψ , |φ } be an incomparable pair of states (|ψ |φ), i.e., |ψ and |φ cannot be transformed to each other with probability one by local transformations and classical communication (LOCC). We show that incomparable states can be multiple-copy transformable, i.e., there can exist a k, such that |ψ ⊗k+1 → |φ ⊗k+1 , i.e., k + 1 copies of |ψ can be transformed to k + 1 copies of |φ with probability one by LOCC but |ψ ⊗n |φ ⊗n ∀n ≤ k. We call such states k-copy LOCC incomparable. We provide a necessary condition for a given pair of states to be k-copy LOCC incomparable for some k. We also show that there exist states that are neither k-copy LOCC incomparable for any k nor catalyzable even with multiple copies. We call such states strongly incomparable. We give a sufficient condition for strong incomparability. We demonstrate that the optimal probability of a conclusive transformation involving many copies, pmax |ψ ⊗m → |φ ⊗m can decrease exponentially with the number of source states m, even if the source state has more entropy of entanglement. We also show that the probability of a conclusive conversion might not be a monotonic function of the number of copies. Fascinating developments in quantum information theory [1] and quantum computing [2] during the past decade has led us to view entanglement as a valued physical resource. Consequently, recent studies have largely been devoted towards its quantification in appropriate limits (finite or asymptotic), optimal manipulation, and transformation properties under local operations and classical communication (LOCC) [3, 4, 5, 6, 7, 8]. Since the specific tasks that can be accomplished with entanglement as a resource is closely related to its transformation properties, it is of importance to know what transformations are allowed under LOCC. Suppose Alice and Bob share a pure state |ψ (source state), which they wish to convert to another entangled state |φ (target state) under LOCC. A necessary and sufficient condition for this transformation to be possible with certainty (denoted by |ψ → |φ) has been obtained by Nielsen [3]. If such a deterministic transformation is not possible but |ψ has at least as many Schmidt coefficients as |φ , then one

Protocols for entanglement transformations of bipartite pure states

Physical Review A, 2003

We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for "pure contraction" transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.

General entanglement-assisted transformation for bipartite pure quantum states

Journal of Physics A: Mathematical and Theoretical, 2007

We introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se. As such, the possibilities of pure entanglement transformations are greatly expanded. We also design an efficient algorithm to detect whether a k × k general catalyst exists for a given entanglement transformation. This algorithm can as well be exploited to witness the existence of standard catalysts.

Some Properties of Three-Party Entangled States and Their Application in Quantum Communication

The Physics of Communication - Proceedings of the XXII Solvay Conference on Physics, 2003

We give a brief overview of work on extending present two-party quantum communication protocols to three-party and multi-party protocols. In particular we discuss the case of threeparty protocols and entanglement-assisted transformations between inequivalent classes of three-particle entangled states (GHZ-states and W-states) which are non-interchangeable under local transformations. We furthermore review possible applications of three-party entangled states.

F eb 2 01 2 Complete set of operational measures for the characterization of 3 − qubit entanglement

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.

Distinguishing different classes of entanglement of three-qubit pure states

The European Physical Journal D

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [19] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.