Optical Interferometry with Quantum Networks

We propose a method for optical interferometry in telescope arrays assisted by quantum networks. In our approach, the quantum state of incoming photons along with an arrival time index are stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglement-assisted parity checks at the expected photon arrival rate allows for direct extraction of the phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme (based on efficient quantum data compression) offers an exponential decrease in required entanglement bandwidth. Experimental implementation is then feasible with near-term technology, enabling optical imaging of astronomical objects akin to well-established radio interferometers and pushing resolution beyond what is practically achievable classically.

Figure 1

Overview of basic operation. Light from a distant source is collected at two sites and stored in quantum memory over time bins digitized by detector bandwidth. Both the quantum state and the arrival time of an incident photon are encoded in a binary qubit code. For example, if the photon arrives in the fifth time bin, corresponding to binary representation 101, we store it in a quantum state with flipped first and third qubits at each node. Decoding of the arrival time is accomplished by nonlocal parity checks assisted by entangled pairs, projecting the memories onto a known entangled state. The phase information can then be extracted without directly interfering the signal from the two memories, thus circumventing transmission losses. Network resources scale only logarithmically with source intensity $\epsilon$.

Figure 2

Minimum number of Bell pairs needed to attain $\parallel F\parallel \ge 1$, corresponding to variance of $\lesssim 1$ in estimating the visibility $g$ as a function of source intensity $\epsilon$. We consider errors in the coding operations parametrized by decreasing $\nu$, as detailed in the main text. Ideally ($\nu =1$), $M\sim 1/\epsilon$ time bins are encoded per block and read out with ${\log }_2(M+1)$ entangled pairs. For sufficiently large errors ($\nu =0.6$), the encoding fails and memoryless operation with the readout of every time bin is recovered, similar to the scheme of Ref. [10].

Figure 3

Generalization to $N>2$ sites in the telescope array. Decoding with a $W$ state collapses the network state to two nodes, and the protocol continues as before. The visibility data are stored in a classical memory until enough events have accumulated to perform a Fourier transform (FT). Using GHZ states instead preserves coherence across the network. Quantum teleporting the memories to one site for convenience, a quantum Fourier transform (QFT) is applied, yielding the desired intensity distribution directly as the probabilities of measurement outcomes.