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arXiv:0707.3917 · Physical Review A

Weak values and continuous-variable entanglement concentration

David Menzies, Natalia Korolkova

Published Dec 17, 2007• 10 citations
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Abstract

We demonstrate a general weak-measurement model which allows Gaussian-preserving entanglement concentration of the two-mode squeezed vacuum. The power of this simple and elegant protocol is through the constraints it places on possible ancilla states and measurement strategies that will allow entanglement concentration. In particular, it is shown how previously discovered protocols of this kind emerge as special examples of the general model described here. Finally, as evidence of its utility, we use it to provide another example of such a protocol.

DOI
10.1103/physreva.76.062310

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We demonstrate a general weak-measurement model which allows Gaussian-preserving entanglement concentration of the two-mode squeezed vacuum. The power of this simple and elegant protocol is through the constraints it places on possible ancilla states and measurement strategies that will allow entanglement concentration. In particular, it is shown how previously discovered protocols of this kind emerge as special examples of the general model described here. Finally, as evidence of its utility, we use it to provide another example of such a protocol.
In this thesis, we are concerned with continuous-variable quantum optical state \nengineering protocols. Such protocols are designed to repair or enhance the nonclassical features of a given state. In particular, we build a weak measurement model \nof Gaussian entanglement concentration of the two mode squeezed vacuum state. \nThis model allows the simultaneous description of all possible ancilla system variations. In addition, it provides an explanation of the Gaussian-preserving property of these protocols while providing a success criterion which links all of the degrees of freedom on the ancilla. Following this, we demonstrate the wider application \nof weak measurements to quantum optical state engineering by showing that they allow probabilistic noiseless amplifi cation of photon number. We then establish a connection between weak measurements and entanglement concentration as a fundamental \nresult of weak measurements on entangled probes. After this, we explore the trade-off between Gaussian and non-Gaussian operations in the preparation of non-Gaussian pure states. In particular, we suggest that an operational cost for an arbitrary non-Gaussian pure state is the largest Fock state required for its approximate preparation. We consider the extent to which this non-Gaussian operational cost can be reduced by applying unitary Gaussian operations. This method relies on the identification of a minimal core state for any target non-Gaussian pure state.
We study entanglement concentration of continuous-variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum (i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter), which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one or on both of the modes and show that local displacements can lead to improved performance of the concentration protocol.
We show how the partial entanglement inherent in a two-mode squeezed vacuum state admits two different teleportation protocols. These two protocols refer to the different kinds of joint measurements that may be made by the sender. One protocol is the recently implemented quadrature phase approach of Braunstein and Kimble [Phys. Rev. Lett. 80,80,80, 869 (1998)]. The other is based on recognizing that a two-mode squeezed vacuum state is also entangled with respect to photon-number difference and phase sum. We show that this protocol can also realize teleportation; however, limitations can arise due to the fact that the photon-number spectrum is bounded from below by zero. Our examples show that a given entanglement resource may admit more than a single teleportation protocol and the question then arises as to what is the optimum protocol in the general case.
Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely, concurrence, of an arbitrary two-qubit pure state via a single fixed measurement setup by exploiting so-called weak measurements and the associated weak values together with the properties of the Laguerre-Gaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol.
We investigate entanglement concentration of continuous-variable Gaussian states by local single-photon subtractions combined with local Gaussian operations. We first analyze the local squeezing-enhanced entanglement-concentration protocol proposed very recently by Zhang and van Loock [arXiv:1103.4500] and discuss the mechanism by which local squeezing before photon subtraction helps to increase the entanglement of the output state of the protocol. We next show that a similar entanglement improvement can be achieved by using local coherent displacements instead of single-mode squeezing.