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arXiv:2204.13129 · Physical Review A

Quantum optical communication in the presence of strong attenuation noise

Francesco Anna Mele, Ludovico Lami, Vittorio Giovannetti

Published Oct 24, 2022• 9 citations
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Abstract

Is quantum communication possible over an optical fiber with transmissivity $\ensuremath{\lambda}\ensuremath{\le}1/2$? The answer is well known to be negative if the environment with which the incoming signal interacts is initialized in a thermal state. However, Lami et al. [Phys. Rev. Lett. 125, 110504 (2020)] found the quantum capacity to be always bounded away from zero for all $\ensuremath{\lambda}>0$, a phenomenon dubbed ``die-hard quantum communication'' (D-HQCOM), provided that the initial environment state can be chosen appropriately, depending on $\ensuremath{\lambda}$. Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $\ensuremath{\lambda}>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel ``trigger signals,'' i.e., signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible due to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibers, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation.

DOI
10.1103/physreva.106.042437

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Is quantum communication possible over an optical fiber with transmissivity \ensuremathλ\ensuremath≤1/2\ensuremath{\lambda}\ensuremath{\le}1/2\ensuremathλ\ensuremath≤1/2? The answer is well known to be negative if the environment with which the incoming signal interacts is initialized in a thermal state. However, Lami et al. [Phys. Rev. Lett. 125, 110504 (2020)] found the quantum capacity to be always bounded away from zero for all \ensuremathλ>0\ensuremath{\lambda}>0\ensuremathλ>0, a phenomenon dubbed die-hard quantum communication'' (D-HQCOM), provided that the initial environment state can be chosen appropriately, depending on $\ensuremath{\lambda}$. Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $\ensuremath{\lambda}>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel trigger signals,'' i.e., signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible due to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibers, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation.
In the absence of quantum repeaters, quantum communication proved to be nearly impossible across optical fibers longer than ≳20 km due to the drop of transmissivity below the critical threshold of 1/2. However, if the signals fed into the fiber are separated by a sufficiently short time interval, memory effects must be taken into account. In this Letter, we show that by properly accounting for these effects it is possible to devise schemes that enable unassisted quantum communication across arbitrarily long optical fibers at a fixed positive qubit transmission rate. We also demonstrate how to achieve entanglement-assisted communication over arbitrarily long distances at a rate of the same order of the maximum achievable in the unassisted noiseless case.
If the transmissivity of an optical fibre falls below a critical value, its use as a reliable quantum channel is known to be drastically compromised. However, if the memoryless assumption does not hold — e.g. when input signals are separated by a sufficiently short time interval — the validity of this limitation is put into question. In this work we introduce a model of optical fibre that can describe memory effects for long transmission lines. We then solve its quantum capacity, two-way quantum capacity, and secret-key capacity exactly. By doing so, we show that — due to the memory cross-talk between the transmitted signals — reliable quantum communication is attainable even for highly noisy regimes where it was previously considered impossible.
A general attenuator ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}}$ is a bosonic quantum channel that acts by combining the input with a fixed environment state $\ensuremath{\sigma}$ in a beam splitter of transmissivity $\ensuremath{\lambda}$. If $\ensuremath{\sigma}$ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for $\ensuremath{\lambda}\ensuremath{\le}1/2$. We study the quantum capacity of these objects for generic $\ensuremath{\sigma}$, proving a number of unexpected results. Most notably, we show that for any arbitrary value of $\ensuremath{\lambda}>0$ there exists a suitable single-mode state $\ensuremath{\sigma}(\ensuremath{\lambda})$ such that the quantum capacity of ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}(\ensuremath{\lambda})}$ is larger than a universal constant c>0c>0c>0. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states $\ensuremath{\sigma}$ such that the quantum capacity of ${\mathrm{\ensuremath{\Phi}}}_{\ensuremath{\lambda},\ensuremath{\sigma}}$ is not monotonic in $\ensuremath{\lambda}$. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.
As quantum information systems mature, efficient and coherent transfer of quantum information through noisy channels becomes increasingly important. We examine how passive environment-assisted quantum communication enhances direct quantum information transfer efficiency. A bosonic pure-loss channel, modeled as transmission through a beam splitter with a vacuum input state at the dark port, has zero quantum capacity when transmissivity is below 50%. Quantum communication through the channel can be enhanced by passive environment assistance, achieved via the selection of an appropriate input state for the ancilla port. Although ideal Gottesman-Kitaev-Preskill (GKP) states enable perfect quantum information transmission at arbitrarily small transmissivity, they are challenging to realize experimentally. We therefore explore more experimentally accessible non-Gaussian ancilla states, such as Fock, cat, and squeezed cat states, and numerically determine the optimal encoding and decoding strategies. We also construct analytical schemes that yield high-fidelity transmission and good information rates.
A phase reference has been a standard requirement in continuous-variable quantum sensing and communication protocols. However, maintaining a phase reference is challenging due to environmental fluctuations, preventing quantum phenomena such as entanglement and coherence from being utilized in many scenarios. We show that quantum communication and entanglement-assisted communication without a phase reference are possible, when a short-time memory effect is present. The degradation in the communication rate of classical or quantum information transmission decreases inversely with the correlation time. Exact solutions of the quantum capacity and entanglement-assisted classical and quantum capacity for pure dephasing channels are derived, where non-Gaussian multipartite-entangled states show strict advantages over usual Gaussian sources. For thermal-loss dephasing channels, lower bounds of the capacities are derived. The lower bounds also extend to scenarios with fading effects in the channel. In addition, for entanglement-assisted communication, the lower bounds can be achieved by a simple phase-encoding scheme on two-mode squeezed vacuum sources, when the noise is large.
The optical signal transmitted on a fiber with thermal noise, attenuation and amplification is studied. The channel is considered as a quantum channel while the signal to be transmitted is classical. The classical information is encoded in a quantum state then it is transmitted in optical fiber. At the receiving end, measurement is performed on the output quantum state to retrieve the classical information. The optimal distribution of the input quantum state achieving the channel capacity is Gaussian. The capacity is characterized by the attenuation/amplification coefficient and thermal noise in the transmission and at the measurement process together by the power of the input. The loss (or attenuation) of an optical fiber usually should be compensated by the amplification. We show that when they coexist, additional noise occurs