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arXiv:quant-ph/0501115 · Physical Review A

Synthesizing arbitrary two-photon polarization mixed states

Tzu-Chieh Wei, Joseph B. Altepeter, David A. Branning, Paul M. Goldbart, Daniel F. V. James, Evan R. Jeffrey, Paul G. Kwiat, Swagatam Mukhopadhyay, Nicholas A. Peters

Published Mar 21, 2005• 50 citations

Abstract

Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: scheme I requires several sets of crystals, while scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states.

DOI: 10.1103/physreva.71.032329

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There has recently been much discussion regarding entanglement transformations in terms of local filtering operations and whether the optimal entanglement for an arbitrary two-qubit state could be realized. We introduce an experimentally realizable scheme for manipulating the entanglement of an arbitrary state of two polarization-entangled qubits. This scheme is then used to provide some perspective to the mathematical concepts inherent in this field with respect to a laboratory environment. Specifically, we look at how to extract enhanced entanglement from systems with a fixed rank, and, in the case where the rank of the density operator for the state can be reduced, show how the state can be made arbitrarily close to a maximally entangled pure state. In this context we also discuss bounds on entanglement in mixed states.

Abstract We have designed and experimentally put to test a protocol to synthesize and characterize pure, two-qubit states encoded in polarization and momentum (path) of light beams. Because these degrees of freedom are common to both classical and quantum light, it was possible to implement our protocol with classical light, thereby offering an advantageous and versatile testing ground. The experimental setup is robust and does not require state-dependent scheme modifications. We exhibited the capabilities of our protocol by generating three types of two-qubit states: Bell states, states with variable phases, and states with variable amplitudes.

A parametric source of polarization-entangled photon pairs with striking spatial characteristics is reported. The distribution of the output electromagnetic

\mathbf{k}

modes excited by spontaneous parametric down-conversion and coupled to the output detectors can be very broad. Using these states realized over a full entanglement ring output distribution, the nonlocal properties of the generated entanglement have been tested by standard Bell measurements and by Ou-Mandel interferometry. A ``mode-patchwork'' technique based on the quantum superposition principle is adopted to synthesize in a straightforward and reliable way any kind of mixed state, of large conceptual and technological interest in modern quantum information. Tunable Werner states and maximally entangled mixed states have indeed been created by this technique and investigated by quantum tomography. A study of the entropic and nonlocal properties of these states has been undertaken experimentally and theoretically, by a unifying variational approach.

We propose a scheme for preparing an arbitrary polarization-entangled mixed state starting from a pure state with location decoherence owing to the path difference. The scheme, using linear optical devices (beam splitter, half wave plate, quarter wave plate) and single-mode optical fibers, is feasible in experiment within current optical technology. We also give a simplified scheme for a special case

\\rho =p|\\psi><\\psi| +(1-p) |\\phi><\\phi|

.