Carrying qubits with particles whose noninformational degrees of freedom are nonfactorable

A directly measurable parameter quantifying effective indistinguishability of particles as a resource for quantum information transfer and processing is proposed. In contrast to commonly used overlap of quantum states of particles, defined only for factorable states, this measure can be generally applied to any joint state of the particles. The relevance of this generalized measure for photons produced in parametric down-conversion has been experimentally verified. The simplest linear-optical quantum-state-transfer protocol, for which this measure directly determines fidelity of the transferred state, was experimentally tested. It has been found that even if some degrees of freedom of two particles are entangled, the particles can still serve as good carriers of qubits.

Figure 1

Scheme of the experiment. FC, fiber couplers; VRC, variable ratio couplers; PM, phase modulators; DL, delay line; D, detectors. The couplers and phase modulators in the state preparation stage enable us to prepare required qubit states (each qubit is represented by a single photon which may propagate in two optical fibers). They do not affect the environmental degrees of freedom. The middle PM applies conditional phase shift depending on the result of the auxiliary measurement. It is a part of the protocol. The rightmost PM and VRC serve for output state tomography.

Figure 2

Dependence of the quality of qubit-state transfer on parameter $D$. Blue circles denote the overlap of output and input states, ${\langle \Psi |}_S{\rho }_T{|\Psi \rangle }_S$. Green squares denote maximal eigenvalues of output states ${\rho }_T$. Straight lines are theoretical predictions. The upper left inset magnifies the area where $D$ is close to zero. The lower right inset shows the measured Hong-Ou-Mandel dip and $R_{\mathrm{rel}}$ denotes relative (normalized) coincidence rate.