Beating the One-Half Limit of Ancilla-Free Linear Optics Bell Measurements

We show that optically encoded two-qubit Bell states can be unambiguously discriminated with a success probability of more than 50% in both single-rail and dual-rail encodings by using active linear-optical resources that include Gaussian squeezing operations. These results are in contrast to the well-known upper bound of 50% for unambiguous discrimination of dual-rail Bell states using passive, static linear optics and arbitrarily many vacuum modes. We present experimentally feasible schemes that improve the success probability to 64.3% in dual-rail and to 62.5% in single-rail for a uniform random distribution of Bell states. Conceptually, this demonstrates that neither interactions that induce nonlinear mode transformations (such as Kerr interactions) nor auxiliary entangled photons are required to go beyond the one-half limit. We discuss the optimality of our single-rail scheme and talk about an application of our dual-rail scheme in quantum communication.

Figure 1

A scheme for DR Bell discrimination that yields a success probability of 64.3%. The Bell states pass through a balanced beam splitter ($\mathcal{B}$), two polarizing beam splitters (${\mathcal{P}}_1$ and ${\mathcal{P}}_2$), and four squeezers (${\mathcal{S}}_1$ to ${\mathcal{S}}_4$) with a squeezing of 5.719 dB each. The output is sent to PNRDs.

Figure 2

In SR, we consider the Bloch-Messiah reduction of a general two-mode squeezing network. The Bell states are passed through a beam splitter ${\mathcal{B}}_1({\theta }_1)$, followed by squeezers ${\mathcal{S}}_1(r_1)$ and ${\mathcal{S}}_2(r_2)$, and finally through a second beam splitter ${\mathcal{B}}_2({\theta }_2)$; ${\theta }_1$ and ${\theta }_2$ are the reflectivity parameters, and $r_1$ and $r_2$ are the squeezing parameters. The output is sent to PNRDs. We only discuss networks with real parameters.