Single photon coding, communication and linear logic

Leandro Aolita, Stephen Patrick Walborn

We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell's inequalities, quantum dense coding, and quantum teleportation.

Stefan Häussler, Peter van Loock

Fiber-based classical communication is all-optical and uses light pulses reamplified and reshaped every 50-100 km in classical repeaters. Most compatible with this would be a quantum communication system which is also all-optical with quantum processing units placed in similar intervals. However, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they would at least depend on sharing complex multi-photon entangled states. Here we propose an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realized in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical infrastructure's long-segment regime. We analyze the performance of our scheme for the Gottesman-Kitaev-Preskill code, including a concatenation with the Steane code, as well as the single-photon quantum parity code for total distances up to 10000 km.

P. M. Intallura

Anton Zeilinger

Hoai Anh Nguyen, Thomas Grange, B. Reznychenko +11 more

Optical logic down to the single photon level holds the promise of data processing with a better energy efficiency than electronic devices [1]. In addition, preservation of quantum coherence in such logical components could lead to optical quantum logical gates [2--4]. Optical logic requires optical non-linearities to enable photon-photon interactions. Non-linearities usually appear for large intensities, but discrete transitions allow for giant non-linearities operating at the single photon level [5], as demonstrated for a single optical mode with cold atomic gases [6, 7], or single two-level systems coupled to light via a tailored photonic environment [8--13]. However optical logic requires two-mode non-linearities [14, 15]. Here we take advantage of the large coupling efficiency and the broadband operation of a photonic wire containing a semiconductor quantum dot (QD) [16] to implement an all-optical logical component, wherein as few as 10 photons per QD lifetime in one mode control the reflectivity of another, spectrally distinct, mode. Whether classical or quantum, optical communication has proven to be the best choice for long distance information distribution. All-optical data processing has therefore raised much interest in recent years, as it would avoid energy and coherence consuming optics-to-electronics conversion steps. Two-ports operation is a necessary requirement for the implementation of any non-trivial optical data processing. This involves a non-linear interaction between two distinct optical modes. Such a functionality operating at the single photon level can be achieved with a giant cross non-linearity obtained via resonant interactions in an atomic-like system featuring discrete energy levels [5].

Simon D. Reiß, Peter van Loock

Bell measurements (BMs) are ubiquitous in quantum information and technology. They are basic elements for quantum commmunication, computation, and error correction. In particular, when performed on logical qubits encoded in physical photonic qubits, they allow for a read-out of stabilizer syndrome information to enhance loss tolerance in qubit-state transmission and fusion. However, even in an ideal setting without photon loss, BMs cannot be done perfectly based on the simplest experimental toolbox of linear optics. Here we demonstrate that any logical BM on stabilizer codes can always be mapped onto a single physical BM perfomed on any qubit pair from the two codes. As a necessary condition for the success of a logical BM, this provides a general upper bound on its success probability, especially ruling out the possibility that the stabilizer information obtainable from only partially succeeding, physical linear-optics BMs could be combined into the full logical stabilizer information. We formulate sufficient criteria to find schemes for which a single successful BM on the physical level will always allow to obtain the full logical information by suitably adapting the subsequent physical measurements. Our approach based on stabilizer group theory is generally applicable to any stabilizer code, which we demonstrate for quantum parity, five-qubit, standard and rotated planar surface, tree, and seven-qubit Steane codes. Our schemes attain the general upper bound for all these codes, while this bound had previously only been reached for the quantum parity code.