Applications of position-based coding to classical communication over quantum channels

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Renyi-2 entropies and conditional quantum entropies.Comment: v4: 44 pages, v4 includes a simpler proof for an upper bound on one-shot entanglement-assisted capacity, also found recently and independently in arXiv:1804.0964

One-shot entanglement-assisted quantum and classical communication

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 that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analogue of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.Comment: 10 pages, 2 figures. Title changed due to new results on the one-shot entanglement-assisted quantum communication. In addition, an error in the previous version regarding the converse proof of the one-shot EAC capacity has been correcte

On converse bounds for classical communication over quantum channels

We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signalling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the $\Upsilon$-information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels we show that the $\Upsilon$-information is a strong converse bound.Comment: v3: published version; v2: 18 pages, presentation and results improve

Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels

Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Renyi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.Comment: 24 pages, 2 figures, v4: final version accepted for publication in Problems of Information Transmissio

Quantum information can be negative

Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned on it's prior information. It turns out to be given by an extremely simple formula, the conditional entropy. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, the sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a primitive "quantum state merging" which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, multiple access channels and multipartite assisted entanglement distillation (localizable entanglement). Negative channel capacities also receive a natural interpretation

Entropic Bounds on Two-Way Assisted Secret-Key Agreement Capacities of Quantum Channels

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

Dualities and identities for entanglement-assisted quantum codes

The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code\u27s information qubits with its ebits. To introduce this notion, we show how entanglement-assisted repetition codes and accumulator codes are dual to each other, much like their classical counterparts, and we give an explicit, general quantum shift-register circuit that encodes both classes of codes. We later show that our constructions are optimal, and this result completes our understanding of these dual classes of codes. We also establish the Gilbert-Varshamov bound and the Plotkin bound for EAQEC codes, and we use these to examine the existence of some EAQEC codes. Finally, we provide upper bounds on the block error probability when transmitting maximal-entanglement EAQEC codes over the depolarizing channel, and we derive variations of the hashing bound for EAQEC codes, which is a lower bound on the maximum rate at which reliable communication over Pauli channels is possible with the use of pre-shared entanglement. © 2013 Springer Science+Business Media New York

Practical route to entanglement-assisted communication over noisy bosonic channels

Entanglement offers substantial advantages in quantum information processing, but loss and noise hinder its applications in practical scenarios. Although it has been well known for decades that the classical communication capacity over lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on the entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity over a very noisy channel and overcomes the fundamental limit of covert communication without entanglement assistance. We then construct receivers for optimum hypothesis testing protocols under discrete phase modulation and for optimum noisy phase estimation protocols under continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radio-frequency and microwave spectral ranges.Comment: 10+6 pages, 13 figures; Close to the published versio