Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity

Abstract

We study the amount of classical communication needed for distributed quantum information processing. In particular, we introduce the concept of "remote preparation" of a quantum state. Given an ensemble of states, Alice's task is to help Bob in a distant laboratory to prepare a state of her choice. We find several examples of an ensemble with an entropy S where the remote preparation can be done with a communication cost lower than the amount (2S) required by standard teleportation. We conjecture that, for an arbitrary N -dimensional pure state, its remote preparation requires 2log 2 N bits of classical communication, as in standard teleportation.

JRSP of three-particle state via three tripartite GHZ class in quantum noisy channels

“…Information stored in quantum system can be teleported from one location to the other with the aid of shared entangled state [3]. Some other processes that exploit quantum entanglement include quantum dense coding [4], quantum secure direct communication [5] and remote state preparation (RSP) [6].…”

“…Information stored in quantum system can be teleported from one location to the other with the aid of shared entangled state [3]. Some other processes that exploit quantum entanglement include quantum dense coding [4], quantum secure direct communication [5] and remote state preparation (RSP) [6].The quantum teleportation can be described as a process by which quantum information is being transmitted from one location to another, with the aid of classical communication and erstwhile shared quantum entanglement between the sending and receiving location. In quantum teleportation, the sender has a particle of unknown state.…”

Randomizing Quantum States: Constructions and Applications

“…Insofar as teleportation [10], or more generally remote state preparation [11], can be interpreted as a method for encrypting quantum states [12,13], our approximate encryption procedure should give rise to an approximate remote state preparation method consuming only half as much communication as teleportation. We report in [9] how our results on randomization provide the basic building block for a protocol capable of sending an arbitrary pure l-qubit quantum state using only l ebits and l + o(l) bits of classical communication.…”

Super-Dense Teleportation using Hyperentangled Photons

“…The two statetransfer techniques described in the previous section are used to send completely general quantum states. However, it is possible to remotely prepare qubit states that are constrained to lie on a great circle of the Poincaré sphere, requiring only a single bit transferred from Alice to Bob [26][27][28] …”