Quantum causal unravelling

Abstract

Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

Quantum space-time marginal problem: global causal structure from local causal information

“…Another interesting problem is the application of the maximum entropy principle in quantum causal inference. Although the existing quantum causal inference protocol is mainly based on process matrix [34][35][36], a possible definition of causal entropy (or space-time entropy) is provided in [13]. Using the maximum causal entropy principle to infer the global causal structure from local causal structures in the process matrix formalism is also of great interest.…”

“…Causal inference is the task of determining the causal structure underlying a set of random variables in the classical world [57], while its extension to the quantum realm is known as quantum causal inference. Recently, there has been a surge of interest in this field, with various approaches being explored based on different quantum causal models [17,[34][35][36][37]. Our focus is on inferring the global causal structure from local causal structures.…”

“…We will show that in this case, there almost always exists a solution to the marginal problem, and the space-time correlations are polygamous in general. Since PDO encodes the quantum causal structure for a given event set, solving the marginal problem can be regarded as the first step to inferring the global causal structure from the given local causal structures, this has many potential applications in quantum causal inference [17,[34][35][36][37]. As an application of our results for the space-time marginal problem, we will explore how to infer the global PDO from the given local PDOs using an information-theoretic approach.…”

Quantum Causal Inference with Extremely Light Touch

“…Similar questions have recently emerged concerning causal relations in quantum processes [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Interventions, like resetting the state of quantum systems, have been considered [23][24][25][26][27][28][29][30][31]. Of particular relevance here is that Ref.…”

Quantifying the entanglement of quantum states under the geometric method

“…Trace norm not only can quantify the entanglement for a multipartitie mixed state, but also it provides a way to quantify the discord [24][25][26][27], the measurement-induced nonlocality [28], asymmetry [29], steering [30] and coherence [31][32][33]. It is also helpful in quantum communication [34,35] and quantum algorithms [36,37].…”