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Register a new userUltimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
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Added by
Vittorio Giovannetti
Publication date
2013
fields
Physics
and research's language is
English
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Optical channels, such as fibers or free-space links, are ubiquitous in todays telecommunication networks. They rely on the electromagnetic field associated with photons to carry information from one point to another in space. As a result, a complete physical model of these channels must necessarily take quantum effects into account in order to determine their ultimate performances. Specifically, Gaussian photonic (or bosonic) quantum channels have been extensively studied over the past decades given their importance for practical purposes. In spite of this, a longstanding conjecture on the optimality of Gaussian encodings has yet prevented finding their communication capacity. Here, this conjecture is solved by proving that the vacuum state achieves the minimum output entropy of a generic Gaussian bosonic channel. This establishes the ultimate achievable bit rate under an energy constraint, as well as the long awaited proof that the single-letter classical capacity of these channels is additive. Beyond capacities, it also has broad consequences in quantum information sciences.
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We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.
We consider sequences of random quantum channels defined using the Stinespring formula with Haar-distributed random orthogonal matrices. For any fixed sequence of input states, we study the asymptotic eigenvalue distribution of the outputs through tensor powers of random channels. We show that the input states achieving minimum output entropy are tensor products of maximally entangled states (Bell states) when the tensor power is even. This phenomenon is completely different from the one for random quantum channels constructed from Haar-distributed random unitary matrices, which leads us to formulate some conjectures about the regularized minimum output entropy.
We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.
As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist pairs of discrete memoryless quantum channels, each of zero quantum capacity, which acquire positive quantum capacity when used together. Here we show that this superactivation phenomenon also occurs in the more realistic setting of optical channels with attenuation and Gaussian noise. This paves the way for its experimental realization and application in real-world communications systems.
We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeffding capacity, that we define similarly to the Holevo capacity, but replacing the relative entropy with the Hoeffding distance. Similarly, our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max-relative entropy in the definition of the divergence radius of a channel.
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