Noiseless Loss Suppression in Quantum Optical Communication

Abstract

We propose a protocol for conditional suppression of losses in direct quantum state transmission over a lossy quantum channel. The method works by noiselessly attenuating the input state prior to transmission through a lossy channel followed by noiseless amplification of the output state. The procedure does not add any noise hence it keeps quantum coherence. We experimentally demonstrate it in the subspace spanned by vacuum and single-photon states, and consider its general applicability.PACS numbers: 03.67. Hk, 42.50.Ex Quantum communication holds the promise of unconditionally secure information transmission [1]. However, the distance over which quantum states of light can be distributed without significant disturbance is limited due to unavoidable losses and noise in optical links. Losses, as well as errors or decoherence, may in principle be overcome by the sophisticated techniques of quantum error correction [2][3][4], entanglement distillation [5][6][7], and quantum repeaters [8,9]. However, these techniques typically require encoding information into complex multimode entangled states, processing many copies of an entangled state, and -even more challenging -using quantum memories [10,11]. In stark contrast with the situation for classical communication, losses in quantum communication cannot be compensated by amplifying the signal, because the laws of quantum mechanics imply that any deterministic phase-insensitive signal amplification is unavoidably accompanied by the addition of noise [12].Very recently, however, the concept of heralded noiseless amplification of light [13] was proposed as a way out, relaxing the deterministic requirement. The noiseless amplification is formally described by a quantum filter g n , where n is the photon number operator and g > 1 denotes the amplification gain. The noiseless amplifier thus modulates amplitudes of Fock states |n by factor g n . This filtration can conditionally increase amplitude of a coherent state |α without adding any noise, g n |α ∝ |gα . Although this cannot be done perfectly because g n is unbounded, faithful noiseless amplification is possible in any finite subspace spanned by the Fock states |n with n ≤ N , albeit with a correspondingly low probability scaling as g −2N in the worst case of input vacuum state. With current technology, it has been proven possible to faithfully noiselessly amplify weak coherent states containing mostly vacuum and single-photon contributions [14][15][16][17].The noiseless amplifier can improve the performance of quantum key distribution protocols [18][19][20][21] and it can also be used to distribute high-quality entanglement over a lossy channel [13,22]. Beyond that, the noiseless amplifier is not useful to suppress losses in direct transmission of arbitrary quantum states because it is not the inverse map of a lossy channel L. As a matter of fact, any superposition of Fock states that is not a coherent state is mapped by L onto a mixed state, and this added noise cannot be eliminated by noiseless amplification.He...

Heralded noiseless amplification and attenuation of non-Gaussian states of light

“…It appears especially useful in the context of quantum key distribution, as it has been theoretically shown to improve the key rate of device-independent discrete-variable protocols [13,14] as well as the range and tolerable excess noise of continuous-variable Gaussian protocols [15][16][17]. Interestingly, the combination of a noiseless attenuator and amplifier at the two ends of a communication line provides a means to reduce the line losses without adding noise [8], which can be exploited in quantum key distribution (note that the noiseless amplifier or attenuator does not necessarily need to be realized in practice, but can be emulated via a postselection procedure [16]). …”

Entanglement-based linear-optical qubit amplifier

“…However in neither of the cases, the entanglement has been restored to the original maximum value due to the presence of the vacuum term |00 00|. Recently, Mičuda et al experimentally demonstrated a rather clever way to eliminate the presence of such term [39]. They considered only vacuum and a fixed polarization single photon state, but the technique can be adopted for qubit amplification as well.…”

Purification of photon subtraction from continuous squeezed light by filtering

“…Neglecting the noiseless attenuation terms ( [19], which can arbitrarily approach the identity at the limit of a small reflectivity R → 0, the conditional state heralded by one-photon detection is,…”