Reliable distribution of quantum entanglement over long distances is a central challenge in quantum information science, fundamentally limited by decoherence in noisy communication channels. In this work, we investigate the asymptotic limits of entanglement distribution across quantum networks utilizing intermediate repeater stations and local operations and classical communication (LOCC). We establish a strict dichotomy: the asymptotic preservation of entanglement over arbitrarily long distances is possible if and only if the underlying quantum channel admits a correctable subspace. For channels lacking such a subspace, we prove that the transmitted state converges exponentially fast to the set of separable states, rendering standard LOCC filtering insufficient. To counteract this exponential degradation, we analyze networks employing parallel channel uses per link. We derive a fundamental lower bound on the physical resource requirements, proving that for channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement. This theoretical limit serves as a stringent benchmark for quantum repeater architectures and underscores the necessity of advanced quantum error-correcting codes, such as qLDPC codes, which show promise in saturating this optimal resource scaling.
Reliable distribution of quantum entanglement over long distances is a central challenge in quantum information science, fundamentally limited by decoherence in noisy communication channels. In this work, we investigate the asymptotic limits of entanglement distribution across quantum networks utilizing intermediate repeater stations and local operations and classical communication (LOCC). We establish a strict dichotomy: the asymptotic preservation of entanglement over arbitrarily long distances is possible if and only if the underlying quantum channel admits a correctable subspace. For channels lacking such a subspace, we prove that the transmitted state converges exponentially fast to the set of separable states, rendering standard LOCC filtering insufficient. To counteract this exponential degradation, we analyze networks employing parallel channel uses per link. We derive a fundamental lower bound on the physical resource requirements, proving that for channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement. This theoretical limit serves as a stringent benchmark for quantum repeater architectures and underscores the necessity of advanced quantum error-correcting codes, such as qLDPC codes, which show promise in saturating this optimal resource scaling.
The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity, which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modeling and the subsequent bounds can be interpreted as the optimal rate within that class.
We investigate the operational limits of entanglement distribution through quantum channels reused without reinitialization. Building on an effective repeated-use channel description, we show that residual excitations left in the channel from previous uses act as a memory source that progressively suppresses coherent quantum transmission. To quantify this limitation, we derive an analytical lower bound on the quantum capacity and combine it with the Holevo-Werner semidefinite-programming upper bound. We also provide an analytical criterion to identify entanglement-breaking channels, with thresholds that depend jointly on chain length and reuse. For perfect-state-transfer chains, the resulting capacity window yields tighter estimates than previous bounds, with the relative improvement becoming substantially more pronounced closer to the entanglement-breaking threshold. Moreover, on the second use, our lower bound certifies a maximal relative timing-error tolerance across all chains with internal memory that lies just below 22.63% and is attained by the three-site chain. We further derive a fundamental relative timing-error threshold of 36.41%, above which we analytically guarantee zero unassisted quantum capacity for every chain with internal memory, independent of the number of uses. These results establish a clear benchmark model for repeated entanglement distribution, and identify timing precision, chain length, and memory accumulation as fundamental constraints on scalable quantum-network architectures.
The quantum capacity of a noisy channel quantifies the maximum rate at which quantum information can be transmitted reliably. For general channels, its evaluation requires an optimization over arbitrarily many channel uses. Degradable channels form a central exception: their capacity is given by the single-letter coherent information, while antidegradable channels have zero capacity. Nevertheless, even for these fundamental classes, it has remained open whether communication above capacity becomes possible when a fixed non-maximal error is tolerated. Here we resolve this problem by proving an exponential strong converse for every finite-dimensional degradable and antidegradable channel: at any rate above capacity, the fidelity of every coding scheme decays exponentially with the number of channel uses. As an immediate consequence, we establish the first all-code exponential strong converse for the quantum erasure channel throughout its full parameter range, strengthening previous results that applied only to almost all codes. We also show that exponential strong-converse bounds are preserved under receiver post-processing. This yields efficiently computable semidefinite-programming bounds for arbitrary finite-dimensional channels, improved bounds for Pauli channels, and an exact exponential strong converse for a nondegradable multilevel amplitude-damping family.
Sending quantum information reliably over long distances is a central challenge in quantum technology in general, and in quantum optics in particular, since most quantum communication relies on optical fibres or free-space links. Here, we address this problem by shifting the focus from the quantity of information sent to the quality of the transmission, i.e. the rate of decay of the transmission error with respect to the number of channel uses. For the general class of teleportation-simulable channels, which includes all channels arising in quantum optical communication, we prove that the single-letter reverse relative entropy of entanglement of the Choi state upper bounds the error exponent of two-way assisted quantum communication - paralleling the celebrated capacity bound of [Pirandola et al., Nat. Comm. (2017)] in terms of the regularised relative entropy of entanglement. Remarkably, for Gaussian channels our bound can be computed efficiently through a convex program with simple constraints involving only finite-dimensional covariance matrices. As a prototypical application, we derive closed-form analytical expressions of our upper bound as well as random-coding-based lower bounds for several one-mode Gaussian channels. Extending recent work [Lami et al., arXiv:2408.07067 (2024)] to infinite-dimensional systems, we further endow the reverse relative entropy of entanglement with an exact operational interpretation in entanglement testing, and show that it characterises the rate of entanglement distillation under non-entangling operations. These findings offer a new perspective on entanglement as a resource and sharpen the theoretical benchmarks for future quantum optical networks.
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number N and allowed average decoding error ε equals the vanishing-error capacity at mean photon number N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.