Quantum Channel Capacities with Passive Environment Assistance

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 show that entanglement plays a crucial role in this problem: indeed, the assisted capacity where the helper is restricted to product states between channel uses is different from the one with unrestricted helper. Furthermore, prior shared entanglement between the helper and the receiver makes a difference, too.Comment: 14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof) changed, updated References and Example 11 added. Comments are welcome

Classical capacities of quantum channels with environment assistance

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [Karumanchi et al., arXiv[quant-ph]:1407.8160], we consider a benevolent third party, i.e. a helper, controlling the environment state, and how the helper's presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, indeed two variants, one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, the two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.Comment: 28 pages, 9 figures. To appear in "Problems of Information Transmission

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity called the bidirectional max-relative entropy of entanglement. We also derive tighter upper bounds on the capacities of bipartite interactions obeying certain symmetries. Observing that reading of a memory device is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a wiretap memory cell. Given a set of point-to-point quantum wiretap channels, the goal of private reading is for an encoder to form codewords from these channels, in order to establish secret key with a party who controls one input and one output of the channels, while a passive eavesdropper has access to one output of the channels. We derive both lower and upper bounds on the private reading capacities of a wiretap memory cell. We then extend these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to a controlled point-to-point channel, which is a particular kind of bipartite interaction.Comment: v3: 34 pages, 3 figures, accepted for publication in Physical Review

Capacities of Quantum Amplifier Channels

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 channels in three different scenarios. First, we establish the capacities of quantum-limited amplifier channels for one of the most general communication tasks, characterized by the trade-off between classical communication, quantum communication, and entanglement generation or consumption. Second, we establish capacities of quantum-limited amplifier channels for the trade-off between public classical communication, private classical communication, and secret key generation. Third, we determine the capacity region for a broadcast channel induced by the quantum-limited amplifier channel, and we also show that a fully quantum strategy outperforms those achieved by classical coherent detection strategies. In all three scenarios, we find that the capacities significantly outperform communication rates achieved with a naive time-sharing strategy.Comment: 16 pages, 2 figures, accepted for publication in Physical Review

Quantum Reverse Shannon Theorem

Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness between sender and receiver is a sufficient auxiliary resource, regardless of the nature of the source, but in the quantum case the requisite auxiliary resources for efficient simulation depend on both the channel being simulated, and the source from which the channel inputs are coming. For tensor power sources (the quantum generalization of classical IID sources), entanglement in the form of standard ebits (maximally entangled pairs of qubits) is sufficient, but for general sources, which may be arbitrarily correlated or entangled across channel inputs, additional resources, such as entanglement-embezzling states or backward communication, are generally needed. Combining existing and new results, we establish the amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient. In particular we find a new single-letter expression for the excess forward communication cost of coherent feedback simulations of quantum channels (i.e. simulations in which the sender retains what would escape into the environment in an ordinary simulation), on non-tensor-power sources in the presence of unlimited ebits but no other auxiliary resource. Our results on tensor power sources establish a strong converse to the entanglement-assisted capacity theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless Eve result, a new single-letter formula for the "spread deficit", better error scaling, and an improved strong converse. v3 and v4 each make small improvements to the presentation and add references. v5 fixes broken reference

Quantum Communication in Rindler Spacetime

A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. We study the impact of this Davies-Fulling-Unruh noise on communication, particularly quantum communication from an inertial sender to an accelerating observer and private communication between two inertial observers in the presence of an accelerating eavesdropper. In both cases, we establish compact, tractable formulas for the associated communication capacities assuming encodings that allow a single excitation in one of a fixed number of modes per use of the communications channel. Our contributions include a rigorous presentation of the general theory of the private quantum capacity as well as a detailed analysis of the structure of these channels, including their group-theoretic properties and a proof that they are conjugate degradable. Connections between the Unruh channel and optical amplifiers are also discussed.Comment: v3: 44 pages, accepted in Communications in Mathematical Physic

Fundamental rate-loss tradeoff for optical quantum key distribution

Since 1984, various optical quantum key distribution (QKD) protocols have been proposed and examined. In all of them, the rate of secret key generation decays exponentially with distance. A natural and fundamental question is then whether there are yet-to-be discovered optical QKD protocols (without quantum repeaters) that could circumvent this rate-distance tradeoff. This paper provides a major step towards answering this question. We show that the secret-key-agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use. Our result has major implications for understanding the secret-key-agreement capacity of optical channels---a long-standing open problem in optical quantum information theory---and strongly suggests a real need for quantum repeaters to perform QKD at high rates over long distances.Comment: 9+4 pages, 3 figures. arXiv admin note: text overlap with arXiv:1310.012

Nonconvexity of private capacity and classical environment-assisted capacity of a quantum channel

The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: The capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is nonconvex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.S.S. acknowledges the support of Sidney Sussex College and European Union under project QALGO (Grant Agreement No. 600700). D.E. has been partially supported by STW, the NWO Vidi grant “Large quantum networks from small quantum devices,” and by the project HyQuNet (Grant No. TEC2012-35673), funded by Ministerio de Econom´ıa y Competitividad (MINECO), Spain