Unrestricted generation of pure two-qubit states and entanglement diagnosis by single-qubit tomography

Abstract

We present an experimental proof-of-principle for the generation and detection of pure two-qubit states which have been encoded in degrees of freedom that are common to both classical-light beams and single photons. Our protocol requires performing polarization tomography on a single qubit from a qubit pair. The degree of entanglement in the qubit pair is measured by concurrence, which can be directly extracted from intensity measurements-or photon counting-entering single-qubit polarization tomography. Entangled qubit pairs are basic units in schemes devised to implement quantum information processes such as quantum communication, quantum cryptography, etc., as well as in schemes designed to address foundational issues of quantum mechanics. The exploitation of entanglement is one of the most challenging goals of quantum information technologies. There are good reasons to believe that entanglement plays a key role in the advantage that quantum circuits would have over classical circuits [1]. Entanglement is however difficult to characterize experimentally. So-called entanglement witnesses are state specific, in the sense that they are tailored to detecting some types of entanglement while they are blind to others. Alternatively, one can rely on entanglement measures, which are designed to be state independent. A prominent example is concurrence, which is defined for any pure, bipartite state Φ as C(Φ) = | Φ|(σ y ⊗ σ y)|Φ * |, where σ y is the Pauli matrix and |Φ * the complex-conjugate of |Φ in the computational basis of the tensor-product space to which Φ belongs. Now, confronted with this measure, the experimentalist sees no obvious way to implement it directly in the laboratory. To begin with, complex conjugation is an unphysical operation, because it does not conserve positive-definiteness. Thus, the only way to obtain C(Φ) from measurements seems to be by means of full tomographic determination of state Φ, which is experimentally demanding and prone to inaccuracies. The evaluation of C(Φ), which nonlinearly depends on the parameters fixing Φ, can then be too inaccurate. Back in 2005, Mintert et al. [2] found a way out of the

Synthesis and characterization of pure, two-qubit states encoded in path and polarization

“…A purity assumption of this kind has been repeatedly confirmed in similar contexts by comparing experimental results to theoretical predictions (see, e.g. [7,11,16,32]).…”

“…Experimentally, Mach-Zehnder and Sagnac interferometers are often used for the preparation and measurement of twoqubit states [32] and two-qubit quantum logic gates [33]. One reason for this choice is that the two qubits can be easily realized as the path and polarization DOFs.…”

“…One reason for this choice is that the two qubits can be easily realized as the path and polarization DOFs. Recently, Gonzales et al [32] proposed and demonstrated a method to generate and characterize pure, two-qubit states with a Mach-Zehndertype interferometer. In practice, the generation procedure proposed in [32] requires painstaking precision to prepare states with arbitrary phases.…”

“…Recently, Gonzales et al [32] proposed and demonstrated a method to generate and characterize pure, two-qubit states with a Mach-Zehndertype interferometer. In practice, the generation procedure proposed in [32] requires painstaking precision to prepare states with arbitrary phases. But the measurement proposal in [32] has even more drawbacks.…”

“…In practice, the generation procedure proposed in [32] requires painstaking precision to prepare states with arbitrary phases. But the measurement proposal in [32] has even more drawbacks. It requires an electronic stabilizing circuit to counteract mechanical perturbations, as well as additional instruments (polarizers) to perform some of the measurements.…”