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 Channel Capacities Per Unit Cost

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 classical communication, entanglement-assisted classical communication, private communication, and quantum communication. For each task, we define the corresponding capacity per unit cost and derive a formula for it analogous to that of the usual capacity. Furthermore, for the special and natural case in which there is a zero-cost state, we obtain expressions in terms of an optimized relative entropy involving the zero-cost state. For each communication task, we construct an explicit pulse-position-modulation coding scheme that achieves the capacity per unit cost. Finally, we compute capacities per unit cost for various bosonic Gaussian channels and introduce the notion of a blocklength constraint as a proposed solution to the long-standing issue of infinite capacities per unit cost. This motivates the idea of a blocklength-cost duality, on which we elaborate in depth.Comment: v3: 18 pages, 2 figure

A Quantum Multiparty Packing Lemma and the Relay Channel

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be "packed" into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.Comment: 20 page

Noisy Feedback and Loss Unlimited Private Communication

Alice is transmitting a private message to Bob across a bosonic wiretap channel with the help of a public feedback channel to which all parties, including the fully-quantum equipped Eve, have completely noiseless access. We find that by altering the model such that Eve's copy of the initial round of feedback is corrupted by an iota of noise, one step towards physical relevance, the capacity can be increased dramatically. It is known that the private capacity with respect to the original model for a pure-loss bosonic channel is at most $- \log(1-\eta)$ bits per mode, where $\eta$ is the transmissivity, in the limit of infinite input photon number. This is a very pessimistic result as there is a finite rate limit even with an arbitrarily large number of input photons. We refer to this as a loss limited rate. However, in our altered model we find that we can achieve a rate of $(1/2) \log(1 + 4 \eta N_S)$ bits per mode, where $N_S$ is the input photon number. This rate diverges with $N_S$, in sharp contrast to the result for the original model. This suggests that physical considerations behind the eavesdropping model should be taken more seriously, as they can create strong dependencies of the achievable rates on the model. For by a seemingly inconsequential weakening of Eve, we obtain a loss-unlimited rate. Our protocol also works verbatim for arbitrary i.i.d. noise (not even necessarily Gaussian) injected by Eve in every round, and even if Eve is given access to copies of the initial transmission and noise. The error probability of the protocol decays super-exponentially with the blocklength.Comment: 7 pages, 2 figure

Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.Comment: v2: 6 pages, 1 figure, final version published in conference proceeding

How China’s demand uncertainty moderates the respondence of operational performance to supply chain integration in automotive industry

This study aims at examining the dynamic response of the relationship between supply chain integration (SCI) and operational performance (OP) to demand uncertainty (DU). Based on a wide spectrum data sample with 357 participants in the China automotive supply chains, threshold regressions are used to examine the dynamic moderating effects. DU was found to moderate supplier integration (SI)–OP and customer integration (CI)–OP relationship. Internal integration (II)–OP relationship did not response to DU. The SI–OP relationship turned from negative to positive as DU increases, and CI–OP relationship responded to DU reversely compare to SI–OP relationship. Scholars now know the moderating effect of DU is not static and monotonic. Both of direction and magnitude of the correlations between SI, CI and OP change when DU changes. Managers of automotive supply chain recognize that their integrations’ strength should be properly managed subject to the level of DU for propose of achieving optimal OP. This study extends the current literature by delivering a field study of China and introducing dynamic capability theory for the first time to examine a dynamic response model that represents the SCI–OP relationships with respect to the DU as a moderating factor