In order to efficiently put quantum technologies into action, we must know the characteristics of the underlying quantum systems and effects. An interesting example is the use of the secret-key-agreement capacity of a quantum channel as a guide and measure for the implementation of quantum key distribution (QKD) and distributed quantum computation. We define the communication task of establishing a secret key over a quantum channel subject to an energy constraint on the input state and while allowing for unlimited local operations and classical communication (LOCC) between a sender and receiver. We then use the energy-constrained squashed entanglement to bound the capacity of the channel for secret-key agreement, and we show that a thermal state input maximizes a relaxation of this bound for phase-insensitive, single-mode Gaussian channels. We also establish improved upper bounds on the energy-constrained secret-key-agreement capacity for a bosonic thermal channel that is not entanglement breaking. We then generalize our results to the multipartite setting and show that the energy-constrained multipartite squashed entanglement bounds the LOCC-assisted private capacity region for a quantum broadcast channel. Next, we define the broadcast amplitude damping channel. In the setting of QKD, we discuss a communication task using the broadcast amplitude damping channel and give bounds on its achievable rate region.
In order to efficiently put quantum technologies into action, we must know the characteristics of the underlying quantum systems and effects. An interesting example is the use of the secret-key-agreement capacity of a quantum channel as a guide and measure for the implementation of quantum key distribution (QKD) and distributed quantum computation. We define the communication task of establishing a secret key over a quantum channel subject to an energy constraint on the input state and while allowing for unlimited local operations and classical communication (LOCC) between a sender and receiver. We then use the energy-constrained squashed entanglement to bound the capacity of the channel for secret-key agreement, and we show that a thermal state input maximizes a relaxation of this bound for phase-insensitive, single-mode Gaussian channels. We also establish improved upper bounds on the energy-constrained secret-key-agreement capacity for a bosonic thermal channel that is not entanglement breaking. We then generalize our results to the multipartite setting and show that the energy-constrained multipartite squashed entanglement bounds the LOCC-assisted private capacity region for a quantum broadcast channel. Next, we define the broadcast amplitude damping channel. In the setting of QKD, we discuss a communication task using the broadcast amplitude damping channel and give bounds on its achievable rate region.
With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energy-constrained, LOCC-assisted private and quantum capacities of quantum channels, which are the maximum rates at which an LOCC-assisted quantum channel can reliably establish a secret key or entanglement, respectively, subject to an energy constraint on the channel input states. We prove that the energy-constrained squashed entanglement of a channel is an upper bound on these capacities. We also explicitly prove that a thermal state maximizes a relaxation of the squashed entanglement of all phase-insensitive, single-mode input bosonic Gaussian channels, generalizing results from prior work. After doing so, we prove that a variation of the method introduced by Goodenough et al. [New J. Phys. 18, 063005 (2016)] leads to improved upper bounds on the energy-constrained secret-key-agreement capacity of a bosonic thermal channel. We then consider a multipartite setting and prove that two known multipartite generalizations of the squashed entanglement are in fact equal. We finally show that the energy-constrained, multipartite squashed entanglement plays a role in bounding the energy-constrained LOCC-assisted private and quantum capacity regions of quantum broadcast channels.
The squashed entanglement of a quantum channel is an additive function of quantum channels, which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication. This quantity has led to an upper bound of log((1+η)/(1-η)) on the capacity of a pure-loss bosonic channel for such a task, where η is the average fraction of photons that make it from the input to the output of the channel. The purpose of this paper is to extend these results beyond the single-sender single-receiver setting to the more general case of a single sender and multiple receivers (a quantum broadcast channel). We employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel, along the way developing several new properties of these measures. We apply our results to the case of a pure-loss broadcast channel with one sender and two receivers.
The squashed entanglement of a quantum channel is an additive function of quantum channels, which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication. This quantity has led to an upper bound of log((1+eta)/(1−eta)) on the capacity of a pure-loss bosonic channel for such a task, where $\\eta $ is the average fraction of photons that make it from the input to the output of the channel. The purpose of this paper is to extend these results beyond the single-sender single-receiver setting to the more general case of a single sender and multiple receivers (a quantum broadcast channel). We employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel, along the way developing several new properties of these measures. We apply our results to the case of a pure-loss broadcast channel with one sender and two receivers.
One of the most sought-after goals in experimental quantum communication is the implementation of a quantum repeater. The performance of quantum repeaters can be assessed by comparing the attained rate with the quantum and private capacity of direct transmission, assisted by unlimited classical two-way communication. However, these quantities are hard to compute, motivating the search for upper bounds. Takeoka, Guha and Wilde found the squashed entanglement of a quantum channel to be an upper bound on both these capacities. In general it is still hard to find the exact value of the squashed entanglement of a quantum channel, but clever sub-optimal squashing channels allow one to upper bound this quantity, and thus also the corresponding capacities. Here, we exploit this idea to obtain bounds for any phase-insensitive Gaussian bosonic channel. This bound allows one to benchmark the implementation of quantum repeaters for a large class of channels used to model communication across fibers. In particular, our bound is applicable to the realistic scenario when there is a restriction on the mean photon number on the input. Furthermore, we show that the squashed entanglement of a channel is convex in the set of channels, and we use a connection between the squashed entanglement of a quantum channel and its entanglement assisted classical capacity. Building on this connection, we obtain the exact squashed entanglement and two-way assisted capacities of the d -dimensional erasure channel and bounds on the amplitude-damping channel and all qubit Pauli channels. In particular, our bound improves on the previous best known squashed entanglement upper bound of the depolarizing channel.
Abstract: We derive an improved upper bound on the two-way-assisted capacities of the qubit amplitude-damping channel with decay probability γ, given by log2[1+(1−γ)γγ/(1−γ)]. It applies to quantum communication, entanglement distribution, private communication, and secret-key agreement, and strictly improves the PLOB relative-entropy bound, the analytic max-relative-entropy bound, and the optimized balanced squashed-entanglement bound. At high damping, a known triple-rail protocol attains more than 99.54% of its leading coefficient. Our method extends sector teleportation simulation to qubits: phase rotations and permutations give exact simulations within fixed-excitation subspaces while preserving the two-level input structure. We determine the exact, additive relative entropy of entanglement of the amplitude-damping resources and the exact regularized entanglement gain at fixed input population. We then derive explicit bounds for generalized amplitude damping, which includes thermal excitation. Combining the amplitude-damping gain with unital and entanglement-breaking channels gives a closed expression that recovers the zero-temperature result and vanishes throughout the entanglement-breaking region. It improves established benchmarks over broad parameter ranges, while the exact entanglement of the generalized resources remains open. Both results admit refinements under an average-excitation constraint. The bounds provide quantitative limits for adaptive communication through relaxing qubits and show how a sector simulation can remain useful beyond channels whose resource entanglement is known exactly.
A gap between achievable rates and converse bounds persists for energy-constrained bosonic communication in the presence of excess noise. We derive a unified adaptive weak-converse bound for thermal attenuation, noisy amplification, and additive Gaussian noise under an unconditional mean transmitted-photon-number constraint. The bound applies to arbitrary adaptive protocols with quantum memories and constrains the two-way quantum, entanglement-distribution, private, and secret-key capacities. It vanishes throughout the entanglement-breaking region and approaches the corresponding PLOB bound at infinite energy. At finite energy, it improves the evaluated Gaussian squashed-entanglement and PLOB bounds in relevant parameter regimes, while comparison with hashing rates quantifies the remaining gap to achievability. The result provides a common energy-dependent benchmark for noisy bosonic Gaussian channels and extends finite-energy converse methods beyond the quantum-limited setting.