Efficient tomography of microwave photonic cluster states

Sequential generation of entangled photonic qubits can provide us with large resource states for quantum computation and communication. However, the generated many-body entanglement is exponentially difficult to characterize using conventional quantum state tomography methods. Here, we propose and experimentally demonstrate an efficient procedure for estimating the density matrix of a sequentially generated string of photons. Because the photons do not interact with each other after they are emitted, the density matrix is constrained to be a matrix product operator with a fixed bond dimension. This means that the number of parameters to be estimated grows only linearly with the number of photonic qubits. Furthermore, since a matrix product operator is fully determined by its local reductions [1], we can choose the measurement bases such that the measurement time is also linear. To demonstrate our tomography scheme, we generate microwave photons in 1D cluster states and reconstruct their density matrices from measurements using a Josephson parametric amplifier.
[1] T. Baumgratz et al., Phys. Rev. Lett. 111, 020401 (2013).