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G. Chiribella and Swati
experimenter has collected some amount of raw data about the values of a set of
variables, and wants to determine whether a certain variable X influences another
variable Y in the set. Since the data are typically subject to noise and fluctuations, the
problem of identifying causal relations is ultimately a statistical inference problem.
Traditionally, causal inference methods have been designed for classical variables. Recent advances in quantum science and engineering motivate an extension
of these methods to the quantum domain. Experimental techniques can now address
individual quantum systems, initialize them in a given quantum state, and subject
them to a variety of quantum measurements. In this context, the presence of causal
dependencies between two quantum systems acquire a concrete practical relevance.
For example, if the interaction of two quantum spins induces a causal dependence
between them, then the state of one spin can be controlled by operating on the other
spin, to some degree that is determined by the strength of the causal relation.
For quantum systems, classical methods of causal inference turn out to be
inadequate. The reason is that such methods assume that randomness can always
be reduced to ignorance about the initial conditions of some additional, latent
variable. This assumption is at odds with the violation of Bell inequalities, which
rules out local realistic models for quantum correlations. For this reason, classical
causal models cannot be applied to the Bell scenario [4]. A similar conclusion also
holds for more general scenarios, including more than two quantum systems, and/or
timelike separations [5, 6].
The breakdown of classical causal inference methods calls for a new, genuinely
quantum formulation of the notions of cause and effect. Several frameworks have
been proposed to date, with different features and sometimes different purposes. The
framework of quantum combs, introduced by Chiribella, D’Ariano, and Perinotti in
a series of works [7–9], describes networks of quantum processes connected with
one another according to a given causal structure. In this framework, one can express
the fact that a given process induces a causal dependence between a quantum system
and another. More broadly, this notion can also be generalized to probabilistic
theories beyond quantum mechanics [10], and to an even broader class of theories
described by symmetric monoidal categories [11, 12]. Frameworks for describing
causal relations in quantum theory and beyond have been developed in [13–
15]. More recently, a quantum framework for describing causal relations between
quantum systems has been developed by Allen et al. [16]. This framework, known
as quantum causal models, can be regarded as an enrichment of the framework
of quantum combs, with new conditions that allow one to express the conditional
independences among quantum variables.
Given a framework for describing causal relationships among quantum variables,
one can develop strategies for identifying such relations. Two interesting examples
were presented in Refs. [17, 18]. In these works, the authors considered the problem
of determining whether two quantum systems, say two photons, are in a spacelike
or timelike configuration. Equivalently, this amounts to determining whether the
states of the two systems are marginals of a bipartite quantum state (spacelike
configuration, corresponding to a past common cause in the joint preparation of the
two systems), or whether the state of one system is obtained from the state of the
G. Chiribella and Swati
experimenter has collected some amount of raw data about the values of a set of
variables, and wants to determine whether a certain variable X influences another
variable Y in the set. Since the data are typically subject to noise and fluctuations, the
problem of identifying causal relations is ultimately a statistical inference problem.
Traditionally, causal inference methods have been designed for classical variables. Recent advances in quantum science and engineering motivate an extension
of these methods to the quantum domain. Experimental techniques can now address
individual quantum systems, initialize them in a given quantum state, and subject
them to a variety of quantum measurements. In this context, the presence of causal
dependencies between two quantum systems acquire a concrete practical relevance.
For example, if the interaction of two quantum spins induces a causal dependence
between them, then the state of one spin can be controlled by operating on the other
spin, to some degree that is determined by the strength of the causal relation.
For quantum systems, classical methods of causal inference turn out to be
inadequate. The reason is that such methods assume that randomness can always
be reduced to ignorance about the initial conditions of some additional, latent
variable. This assumption is at odds with the violation of Bell inequalities, which
rules out local realistic models for quantum correlations. For this reason, classical
causal models cannot be applied to the Bell scenario [4]. A similar conclusion also
holds for more general scenarios, including more than two quantum systems, and/or
timelike separations [5, 6].
The breakdown of classical causal inference methods calls for a new, genuinely
quantum formulation of the notions of cause and effect. Several frameworks have
been proposed to date, with different features and sometimes different purposes. The
framework of quantum combs, introduced by Chiribella, D’Ariano, and Perinotti in
a series of works [7–9], describes networks of quantum processes connected with
one another according to a given causal structure. In this framework, one can express
the fact that a given process induces a causal dependence between a quantum system
and another. More broadly, this notion can also be generalized to probabilistic
theories beyond quantum mechanics [10], and to an even broader class of theories
described by symmetric monoidal categories [11, 12]. Frameworks for describing
causal relations in quantum theory and beyond have been developed in [13–
15]. More recently, a quantum framework for describing causal relations between
quantum systems has been developed by Allen et al. [16]. This framework, known
as quantum causal models, can be regarded as an enrichment of the framework
of quantum combs, with new conditions that allow one to express the conditional
independences among quantum variables.
Given a framework for describing causal relationships among quantum variables,
one can develop strategies for identifying such relations. Two interesting examples
were presented in Refs. [17, 18]. In these works, the authors considered the problem
of determining whether two quantum systems, say two photons, are in a spacelike
or timelike configuration. Equivalently, this amounts to determining whether the
states of the two systems are marginals of a bipartite quantum state (spacelike
configuration, corresponding to a past common cause in the joint preparation of the
two systems), or whether the state of one system is obtained from the state of the