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arXiv:1609.04200 · Optics Express

Transmitting more than 10 bit with a single photon

Tristan B. H. Tentrup, Thomas Hummel, Tom A. W. Wolterink, Ravitej Uppu, Allard P. Mosk, Pepijn W. H. Pinkse

Published Feb 2, 2017• 17 citations
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Abstract

Encoding information in the position of single photons has no known limits, given infinite resources. Using a heralded single-photon source and a spatial light modulator (SLM), we steer single photons to specific positions in a virtual grid on a large-area spatially resolving photon-counting detector (ICCD). We experimentally demonstrate selective addressing any location (symbol) in a 9072 size grid (alphabet) to achieve 10.5 bit of mutual information per detected photon between the sender and receiver. Our results can be useful for very-high-dimensional quantum information processing.

DOI
10.1364/oe.25.002826

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Encoding information in the position of single photons has no known limits, given infinite resources. Using a heralded single-photon source and a spatial light modulator (SLM), we steer single photons to specific positions in a virtual grid on a large-area spatially resolving photon-counting detector (ICCD). We experimentally demonstrate selective addressing any location (symbol) in a 9072 size grid (alphabet) to achieve 10.5 bit of mutual information per detected photon between the sender and receiver. Our results can be useful for very-high-dimensional quantum information processing.
Single photons are the carrier of choice in many quantum information processing protocols. Encoding information in a high-dimensional Hilbert space allows for the transfer of more than one bit of information per photon. We use a spatial light modulator (SLM) to direct the single photons to distinct positions of a virtual grid in the Fourier plane of the SLM. An electron-multiplying CCD (EMCCD) was used to detect the position of the photon at the receiver side. After analyzing the data, we conclude that, in contrast to an intensified CCD (ICCD), an EMCCD is not suited to detect the position of one single photon impinging on the camera in a single-shot measurement.
Abstract Most quantum key distribution protocols using a two-dimensional basis, such as HV polarization as first proposed by Bennett and Brassard in 1984, are limited to a key generation density of 1 bit per photon. We increase this key density by encoding information in the transverse spatial displacement of the used photons. Employing this higher-dimensional Hilbert space together with modern single-photon-detecting cameras, we demonstrate a proof-of-principle large-alphabet quantum key distribution experiment with 1024 symbols and a shared information between sender and receiver of 7 bit per photon.
The high-dimensional encoding of single photons can offer various possibilities for enhancing quantum information processing. This work experimentally demonstrates the quantum interference of an engineered multidimensional quantum state through the space-division multiplexing of a heralded single-photon state with a spatial light modulator (SLM) and spatial-mode mixing of a single photon through a long multimode fiber (MMF). In our experiment, the heralded single photon generated from a warm 87 Rb atomic ensemble was bright, robust, and long-coherent. The multidimensional spatial quantum state of the long-coherent single photon was transported through a 4-m-long MMF and arbitrarily controlled using the SLM. We observed the quantum interference of a single-photon multidimensional spatial quantum state with a visibility of >95%. These results may have potential applications in quantum information processing, for example, in photonic variational quantum eigensolve with high-dimensional single photons and realizing high information capacity per photon for quantum communication.
Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum-selected passively via a beam splitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver, who similarly performs a random measurement in one of the two bases. In this implementation, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. To assess the scalability of this spatial-mode encoding scheme, we theoretically show that using a brighter entangled photon source along with next-generation single-photon cameras - featuring improved quantum efficiency, timing and spatial resolution - this approach could achieve 9 bits per photon at 2000 spatial modes, and a bit rate of over 700 Mb/s at 4400 modes while accounting for finite-key effects. These results quantify the opportunities and performance bounds of spatially encoded, entanglement-based QKD and provide a benchmark for future high-dimensional quantum communication systems.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
We address the problem of how efficiently information can be encoded into and read out reliably from a passive reflective surface that encodes classical data by modulating the amplitude and phase of incident light. We show that nature imposes no fundamental upper limit to the number of bits that can be read per expended probe photon and demonstrate the quantum-information-theoretic trade-offs between the photon efficiency (bits per photon) and the encoding efficiency (bits per pixel) of optical reading. We show that with a coherent-state (ideal laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly optimistic model for commercial CD and DVD drives), the highest photon efficiency achievable in principle is about 0.5 bits read per transmitted photon. We then show that a coherent-state probe can read unlimited bits per photon when the receiver is allowed to make joint (inseparable) measurements on the reflected light from a large block of phase-modulated memory pixels. Finally, we show an example of a spatially entangled nonclassical light probe and a receiver design---constructible using a single-photon source, beam splitters, and single-photon detectors---that can in principle read any number of error-free bits of information. The probe is a single photon prepared in a uniform coherent superposition of multiple orthogonal spatial modes, i.e., a WWW state. The code and joint-detection receiver complexity required by a coherent-state transmitter to achieve comparable photon efficiency performance is shown to be much higher in comparison to that required by the WWW-state transceiver, although this advantage rapidly disappears with increasing loss in the system.