The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. In particular, we find analytically and numerically the quantum and classical capacities for a large family of quantum channels and show that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics.
Several theoretical Deterministic Secure Direct Bidirectional Communication protocols are generalized to improve their capacities by introducing the superdense-coding in the case of high-dimension quantum states.
We show that entangling capacities based on the Jamiolkowski isomorphism may be used to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Therefore, for these definitions, the relations which have been previously shown for two-qubit unitaries also hold for arbitrary dimensions. These results are closely related to the theory of the entanglement-assisted capacity of channels. We also present more general methods for producing ensembles for communication from initial states for entanglement creation.
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a new bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.
Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising properties: 1) simulating it with the assistance of unlimited EPR pairs requires far more communication than with a better choice of entangled state, and 2) its communication capacity is far lower than its capacity to create entanglement. This suggests that 1) unlimited EPR pairs are not the most general model of entanglement assistance for two-party communication…
Unitary gates are an interesting resource for quantum communication in part because they are always invertible and are intrinsically bidirectional. This paper explores these two symmetries: time-reversal and exchange of Alice and Bob. We will present examples of unitary gates that exhibit dramatic separations between forward and backward capacities (even when the back communication is assisted by free entanglement) and between entanglement-assisted and unassisted capacities, among many others. Along the way, we will give a general time-reversal rule for relating the capacities of a unitary gat…
A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we sh…
We demonstrate superadditivity in the communication capacity of a binary alphabet consisting of two nonorthogonal quantum states. For this scheme, collective decoding is performed two transmissions at a time. This improves upon the previous schemes of Sasaki et al. [Phys. Rev. A 58, 146 (1998)] where superadditivity was not achieved until a decoding of three or more transmissions at a time. This places superadditivity within the regime of a near-term laboratory demonstration. We propose an experimental test based upon an alphabet of low photon-number coherent states where the signal decoding i…
Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems, and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introd…
We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, so called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an a…
For quantum states of two subsystems, entanglement measures are related to capacities of communication tasks -- highly entangled states give higher capacity of transmitting classical as well as quantum information. However, we show that this is no more the case in general: quantum capacities of multi-access channels, motivated by communication in quantum networks, do not have any relation with genuine multiparty entanglement measures. Along with revealing the structural richness of multi-access channel capacities, this gives us a tool to classify multiparty quantum states from the perspective …
Reciprocal pairs of quantum channels are defined as completely positive transformations which admit a rigid, distance-preserving, yet not completely-positive transformation that allows to reproduce the outcome of one from the corresponding outcome of the other. From a classical perspective these transmission lines should exhibit the same communication efficiency. This is no longer the case in the quantum setting: explicit asymmetric behaviours are reported studying the classical communication capacities of reciprocal pairs of depolarizing and Weyl-covariant channels.
Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an en…
We analyze different aspects of multiparty communication over quantum memoryless channels and generalize some of key results known from bipartite channels to that of multiparty scenario. In particular, we introduce multiparty versions of minimal subspace transmission fidelity and entanglement transmission fidelity. We also provide alternative, local, versions of fidelities and show their equivalence to the global ones in context of capacity regions defined. The equivalence of two different capacity notions with respect to two types of the fidelities is proven. In analogy to bipartite case it i…
We study the communication capacities of bosonic broadband channels in the presence of different sources of noise. In particular we analyze lossy channels in presence of white noise and thermal bath. In this context, we provide a numerical solution for the entanglement assisted capacity and upper and lower bounds for the classical and quantum capacities.
Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study the…
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical capacity, quantum capacity, and private classical capacity are continuous, with the variation on arguments epsilon apart bounded by a simple function of epsilon and the channel's output dimension. Our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state; the bound is linear in the …
Using the Lieb-Robinson inequality and the continuity property of the quantum capacities in terms of the diamond norm, we derive an upper bound on the values that these capacities can attain in spin-network communication i.i.d. models of arbitrary topology. Differently from previous results we make no assumptions on the encoding mechanisms that the sender of the messages adopts in loading information on the network.
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory intractable. As a result communication capacities are not known, even for transmission between two users connected by an electromagnetic waveguide subject to gaussian noise. Here we present an exactly solvable model of communications with a fully quantum electromagnetic field. This allows us to find explicit expressions for all the point-to-point capacities…
We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its efficiency by studying its performance for most well known single qubit noisy channels and for the generalised Pauli channel in arbitrary finite dimension.
Quantum amplifier channels are at the core of several physical processes. Not only do they model the optical process of spontaneous parametric down-conversion, but the transformation corresponding to an amplifier channel also describes the physics of the dynamical Casimir effect in superconducting circuits, the Unruh effect, and Hawking radiation. Here we study the communication capabilities of quantum amplifier channels. Invoking a recently established minimum output-entropy theorem for single-mode phase-insensitive Gaussian channels, we determine capacities of quantum-limited amplifier chann…
We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.
In present-day quantum communications, one of the main problems is the lack of a quantum repeater design that can simultaneously secure high rates and long distances. Recent literature has established the end-to-end capacities that are achievable by the most general protocols for quantum and private communication within a quantum network, encompassing the case of a quantum repeater chain. However, whether or not a physical design exists to approach such capacities remains a challenging objective. Driven by this motivation, in this work, we put forward a design for continuous-variable quantum r…
We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We s…
The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels experience noise which is modelled better by errors that are correlated between separate channel uses. In this paper, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channe…
Entanglement shared between the two ends of a quantum communication channel has been shown to be a useful resource in increasing both the quantum and classical capacities for these channels. The entanglement-assisted capacities were derived assuming an unlimited amount of shared entanglement per channel use. In this paper, bounds are derived on the minimum amount of entanglement required per use of a channel, in order to asymptotically achieve the capacity. This is achieved by introducing a class of entanglement-assisted quantum codes. Codes for classes of qubit channels are shown to achieve t…
In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a quantum channel, but not yet fully understood in protocols with quantum repeaters. Here we solve this problem bounding the ultimate rates for transmitting quantum information, entanglement and secret keys via quantum repeaters. We derive single-letter upper bounds for the end-to-end capacities achievable by the most general (adaptive) protocols of quantum and pri…
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply t…
We consider the communication of classical and quantum information between two arbitrary observers in asymptotically flat spacetimes (possibly containing black holes) and investigate what is the energy cost for such information transmission. By means of localized two-level quantum systems, sender and receiver can use a quantum scalar field as a communication channel. As we have already shown in a previous paper, such a channel has non-vanishing classical capacity as well as entanglement-assisted classical and quantum capacities. Here we will show that the change in the expectation value of the…
A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's potential for communication. In this short review, I summarize what is known about the various capacities of a quantum channel, including a discussion of the relevant additivity questions. I also give some indication of potentially interesting directions for future research.
Communication over a noisy channel is often conducted in a setting in which different input symbols to the channel incur a certain cost. For example, for bosonic quantum channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a quantum channel such as classica…
Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity m…
Quantum channels are known to provide qualitatively better information transfer capacities over their classical counterparts. Examples include quantum cryptography, quantum dense coding, and quantum teleportation. This is a short review on paradigmatic quantum communication protocols in both bipartite as well as multipartite scenarios.
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. By constructing an upperbound based on the relative entropy of entang…
Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as cl…
We find a strong-converse bound on the private capacity of a quantum channel assisted by unlimited two-way classical communication. The bound is based on the max-relative entropy of entanglement and its proof uses a new inequality for the sandwiched Rényi divergences based on complex interpolation techniques. We provide explicit examples of quantum channels where our bound improves both the transposition bound (on the quantum capacity assisted by classical communication) and the bound based on the squashed entanglement introduced by Takeoka et al.. As an application we study a repeater version…
We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.
We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, $Q_2$, exceeds their unassisted one-shot Holevo capacity $C_H$. These channels may be thought of as having a data input and output, along with a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly inferred by a classically coordinated processing of 1) the control output, and 2) a reference system ent…
We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum key distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels.
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical …
We present a communication protocol for the erasure channel assisted by backward classical communication, which achieves a significantly better rate than the best prior result. In addition, we prove an upper bound for the capacity of the channel. The upper bound is smaller than the capacity of the erasure channel when it is assisted by two-way classical communication. Thus, we prove the separation between quantum capacities assisted by backward classical communication and two-way classical communication.
We implement a mechanism - originally proposed as a model for the large memory storage capacity of black holes - in quantum neural networks and show that an exponentially increased capacity of pattern storage and recognition is achieved in certain critically excited states, without involvement of synaptic plasticity. We consider a simple network of N interconnected quantum neurons with weak excitatory synaptic connections. We show that for frozen synaptic weights there exist the critical states of enhanced memory storage capacity. These states are achieved thanks to the high excitation levels …
This paper establishes a general theory of energy-constrained quantum and private capacities of quantum channels. We begin by defining various energy-constrained communication tasks, including quantum communication with a uniform energy constraint, entanglement transmission with an average energy constraint, private communication with a uniform energy constraint, and secret key transmission with an average energy constraint. We develop several code conversions, which allow us to conclude non-trivial relations between the capacities corresponding to the above tasks. We then show how the regular…
We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we pre…
We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper who can set its initial state such as to assist sender and receiver of the communication link. (The case of a malicious environment, also known as jammer, or arbitrarily varying channel, is essentially well-understood and comprehensively reviewed.) Here, after setting out precise definitions, focussing on the problem of quantum communication, we …
In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we want to optimally use a quantum channel for general communication purpose. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity, and it is largely unknown if this could lead to an superadditive double or triple resource capacity. For example, if a channel has an additive classical and quantum capacit…
We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent communication, we are able to generalize super-dense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulae for the classical and quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed amount of entanglement per use.
We propose two types of quantum dense coding communication networks with optical continuous variables, in which a quadripartite entangled state of the optical field with totally three-party correlations of quadrature amplitudes is utilized. In the networks, the exchange of information between any two participants can be manipulated by one or two of the remaining participants. The channel capacities for a variety of communication protocols are numerically calculated. Due to the fact that the quadripartite entangled states applied in the communication systems have been successfully prepared alre…
Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism, we formulate different classical capacities for a bi-partite quantum process. We find that a one-way communication protocol through an arbitrary process cannot outperform a causally separable process, i.e., we can send at most one bit per qubit. Next, we study bi-directional communication through a causally separable process. Our result shows, a bi-directio…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and re…
