A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel
M. E. Shirokov
备注：
17 pages, generalizations to infinite dimensional quantum channels with linear constraints have been added. arXiv admin note: text overlap with arXiv:1106.3297
发表信息：
Problems of Information Transmission, 48:2 (2012), 85-101
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the above-mentioned capacities of a quantum channel implies that the $χ$-essential part of this channel is a c-q channel (the $χ$-essential part is a restriction of a channel obtained by discarding all input states useless for transmission of classical information).
The above observations are generalized to infinite dimensional quantum channels with linear constraints by using the obtained conditions for coincidence of the quantum mutual information and the constrained Holevo capacity.
Werner states have a host of interesting properties, which often serve to illuminate the unusual properties of quantum information. Starting from these states, one may define a family of quantum channels, known as the Holevo-Werner channels, which themselves afford several unusual properties. In this paper we use the teleportation covariance of these channels to upper bound their two-way assisted quantum and secret-key capacities. This bound may be expressed in terms of relative entropy distances, such as the relative entropy of entanglement, and also in terms of the squashed entanglement. Mos…
We give a capacity formula for the classical communication over a noisy quantum channel, when local operations and global permutations allowed in the encoding and bipartite states preshared between the sender and the receiver. The two endpoints of this formula are the Holevo capacity (without entanglement assistance) and the entanglement-assisted capacity (with unlimited entanglement assistance). What's more, we show that the capacity satisfies the strong converse property and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. We prove …
The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. According to the applications of entropic uncertainty relation, studying and trying to improve the bound of this relation is of great importance. Uncertainty bound can be altered by considering an extra quantum system as the quantum memory $B$ which is …
There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional min-entropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is sho…
Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes assisted zero-error quantum capacity depends only on the non-commutative bipartite graph of the channel and the one-shot case can be computed efficiently by semidefinite programming (SDP). As an example, the activated PPTp codes assisted zero-error quantum capacity is carefully studied. We then present a general SDP upper bound $Q_Γ$ of quantum capacity and show it is always…
Entanglement underpins a variety of quantum-enhanced communication, sensing, and computing capabilities. Entanglement-assisted communication (EACOMM) leverages entanglement pre-shared by communication parties to boost the rate of classical information transmission. Pioneering theory works showed that EACOMM can enable a communication rate well beyond the ultimate classical capacity of optical communications, but an experimental demonstration of any EACOMM advantage remains elusive. Here, we report the implementation of EACOMM surpassing the classical capacity over lossy and noisy bosonic chann…
In the last two decades, many quantum optics experiments have demonstrated small-scale quantum information processing applications with several photons. Beyond such proof-of-principle demonstrations, efficient preparation of large, but definite, numbers of photons is of great importance for further scaling up and speeding up photonic quantum information processing. Typical single-photon generation techniques based on nonlinear parametric processes face challenges of probabilistic generation. Here we demonstrate efficient synchronization of photons from multiple nonlinear parametric heralded si…
In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $ρ$ drawn from a known ensemble (but without knowing what $ρ$ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of $ρ$. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assisted visible compression…
Tulane University（杜兰大学）；United States Army Research Laboratory（美国陆军研究实验室）
We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidel…
Pre-shared entanglement can significantly boost communication rates in the regime of high thermal noise, and a low-brightness transmitter. In this regime, the ratio between the entanglement-assisted capacity and the Holevo capacity, the maximum reliable-communication rate permitted by quantum mechanics without any pre-shared entanglement as a resource, is known to scale as $\log(1/N_S)$, where $N_S \ll 1$ is the mean transmitted photon number per mode. This is especially promising in enabling a large boost to radio-frequency communications in the weak-transmit-power regime, by exploiting pre-s…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more accurate and complete theory with new and more powerful possibilities for information processing. The goal of both classical and quantum information theory is to quantify the optimal rates of interconversion of different resources. These rates are usually characterized in terms of entropies. However, nonadditivity of many entropic formulas often makes finding a…
