Genuine multiparty quantum entanglement suppresses multiport classical information transmission

Abstract

We establish a universal complementarity relation between the capacity of classical information transmission by employing a multiparty quantum state as a multiport quantum channel, and the corresponding genuine multipartite entanglement. The classical information transfer is from a sender to several receivers by using the quantum dense coding protocol with the multiparty quantum state shared between the sender and several receivers. The relation is derived when the multiparty entanglement is the relative entropy of entanglement as well as when it is the generalized geometic measure. The relation holds for arbitrary pure or mixed quantum states of an arbitrary number of parties in arbitrary dimensions.The discoveries of the quantum communication strategies, beginning with the protocols of quantum dense coding [1], quantum teleportation [2] and quantum key distribution [3], have revolutionized the way we think about modern communication schemes. The importance of such protocols lies in the fact that they can efficiently transmit classical or quantum information in a way that is better than what is possible by using classical protocols. Such quantum communication schemes have already been realized experimentally, and in particular, experimental quantum dense coding have been reported in several systems including photonic states, ion traps, and nuclear magnetic resonance [4]. The protocols were initially introduced for communication between two separated parties. This is true for the theoretical discussions of these protocols as well as for the experimental demonstrations of the same. It has already been established that in the case of such bipartite communication schemes between a sender and a receiver, shared quantum correlations play a key role.

From unextendible product bases to genuinely entangled subspaces

“…From a practical point of view, genuinely entangled subspaces are natural candidates for quantum error correction codes, where subspaces with well established properties are utilized [44]. On the other hand, when treated as sources of genuinely entangled multipartite states, they may also find applications in other areas of quantum information theory, where the usefulness of such states has already been recognized, such as, e.g., quantum metrology [7][8][9], dense coding [45], or key distribution [46].…”

Separability and entanglement in superpositions of quantum states

“…Quantum entanglement [1][2][3] is regarded as an important resource because it finds applications in several information processing protocols, like quantum teleportation [4,5], quantum dense coding [6][7][8][9][10][11], and quantum key distribution [12,13]. Entanglement in quantum states of shared systems is a result of the superposition principle of quantum physics.…”

Monogamy of Quantum Correlations - A Review

“…There exists no-go theorems which place parallel restrictions such as monogamy of Bell inequality violation [48,49] and exclusion principle of classical information transmission over quantum channels [50] (cf. [51][52][53][54]). More precisely, within the consideration of a multiparty set-up, for example, of an editor with several reporters, if the shared quantum state between the editor and a single reporter violates a Bell inequality [55,56] or is quantum dense codeable [57], then the rest of the channels shared between the editor and the other reporters are prohibited from possessing the same quantum advantage.…”