We consider the communication of classical and quantum information between two arbitrary observers in asymptotically flat spacetimes (possibly containing black holes) and investigate what the energy cost is 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 nonvanishing classical capacity as well as entanglement-assisted classical and quantum capacities. Here we will show that the change in the expectation value of the energy of the system during the communication process can be separated in (i) a contribution coming from the particle creation due to the change of the spacetime, (ii) a contribution associated with the energy needed to switch on or off each qubit, and (iii) a term which comes from the communication process itself. For the quantum channel considered here, we show that the extra energy cost needed for communication vanishes. As a result, if one has already created a system of qubits for some specific task (e.g., quantum computation), one can also reliably convey information between its parts with no extra energy cost. We conclude the paper by illustrating the form of the channel capacities and energy contributions in two paradigmatic cases in Minkowski spacetime: (i) sender and receiver in inertial motion and (ii) sender in inertial motion while the receiver is uniformly accelerated.
We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where information bits become useless after a certain time. Trailing the capacity results obtained recently for certain queue-channels, this paper aims to construct practical channel codes for the erasure queue-channel (EQC)—a channel characterized by highly correlated erasures, governed by the underlying queuing dynamics. Our main contributions in this paper are twofold: (i) We propose a generic ‘wrapper’ based on interleaving across renewal blocks of the queue to convert any capacity-achieving code for a memoryless erasure channel to a capacity-achieving code for the EQC. Next, due to the complexity involved in implementing interleaved systems, (ii) we study the performance of LDPC and Polar codes without any interleaving. Motivated by the empirical performance, we show that standard Arıkan’s Polar transform polarizes the M/M/1 EQC.
We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i)
N-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the
N-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.