Quantum correlations and global coherence in distributed quantum computing

Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the classical formalism. Here, we consider the efficiency of quantum computation protocols compared to classical ones as a benchmark for separating quantum and classical resources and argue that the computational advantage of collaborative quantum protocols in the discrete variable domain implies the nonclassicality of correlations. By analyzing a toy model, it turns out that this argument implies the existence of quantum correlations distinct from entanglement and discord. We characterize such quantum correlations in terms of the net global coherence resources inherent within quantum states and show that entanglement and discord can be understood as special cases of our general framework. Finally, we provide an operational interpretation of such correlations as those allowing two distant parties to increase their respective local quantum computational resources only using locally incoherent operations and classical communication.

Figure 1

Geometrical illustration of nonclassicality within the context of coherence theory. A classical process (the zigzag solid black line) is represented as an efficient composition of strictly incoherent operations evolving inside the set of incoherent states at all times. A quantum process from a classical observer's point of view (the green curve), on the other hand, is equivalent to a strict incoherent operation. However, it may involve generation and consumption of coherence at some stages and, thus, it may partially be traversing outside the incoherent set. Such maps may or may not be efficiently representable as a composition of USI operations.

Figure 2

The schematic of a nonlocal deterministic quantum computation with two qubits (NDQC2). A client, Charlie, who does not possess any quantum processors aims to estimate the quantity $\iota =\mathrm{Tr}{\widehat{U}}_{\mathrm{A}}·\mathrm{Tr}{\widehat{U}}_{\mathrm{B}}/2^{n_{\mathrm{A}}+n_{\mathrm{B}}}$. This is believed to be hard to perform on a classical computer. Therefore, he asks two servers, Alice and Bob, who are capable of performing unitary transformations and making destructive measurements to realize the controlled unitaries ${\widehat{U}}_{\mathrm{X}}^{\mathrm{cont}}$ ($\mathrm{X}=\mathrm{A},\mathrm{B}$). The servers are forbidden to communicate and do not have access to any sources of quantum states. Charlie then sends strictly classical states to the servers and receives the results of the measurements of the Pauli operators as per Eq. (7). By manipulating the received data, he is able to efficiently estimate $\iota$. Depending on his choice of state, Charlie is also able to hide the local estimates from Alice and Bob without reducing his global computational power.