Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1803.00369 · New Journal of Physics

Two-qubit causal structures and the geometry of positive qubit-maps

Jonas M. Kübler, Daniel Braun

Published Jul 26, 2018• 9 citations
arXivHTMLPDF

Abstract

We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.

DOI
10.1088/1367-2630/aad612

Related papers

Causal confusion in quantum systems: distinguishing direct cause and common cause

Krisztina Tolotti, Riley Blank-Matthews, Arthur J. Parzygnat

The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.

quant-pharXiv:2610.10004•Oct 8, 2026•0 citations

Realization of algorithmic identification of cause and effect in quantum correlations

Zhaoan Wang, Yu Meng, Zhenghao Liu +10 more

Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple subfields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation of Reichenbach's principle and enabling causal inference with only observational data. However, it is still not clear how quantum causal inference can provide operational advantages in general cases. Here, we have devised a photonic setup and experimentally realized an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario, thus revealing a universal quantum advantage in causal inference over its classical counterpart. We further demonstrate the explainability and stability of our causal discovery method, which is widely sought in data processing algorithms. Employing a fully observational approach, our result paves the way for studying quantum causality in general settings.

arXiv:2304.10192•Physical Review A•Jan 3, 2024•0 citations

Quantum observation scheme universally identifying causalities from correlations

Chenguang Zhang, Yuexian Hou, Dawei Song

It has long been recognized as a difficult problem to determine whether the observed statistical correlations between two classical variables arise from causality or from common causes. Recent research has shown that, in a quantum theoretical framework, the mechanisms of entanglement and quantum coherence provide advantages in tackling this problem. In some particular cases, quantum common causes and quantum causality can be effectively distinguished by using observations alone. However, these solutions do not apply to all cases. There still exist a large class of cases in which quantum common causes and quantum causality cannot be distinguished. In this paper, along the line of considering unitary transformation as causality in the quantum world, we formally show that quantum common causes and quantum causality are universally separable. Based on the analysis, we further provide a general method to discriminate the two.

arXiv:1903.03449•Physical Review A•Jun 3, 2020•6 citations

Discrimination between quantum common causes and quantum causality

Mingdi Hu, Yuexian Hou

In classic cases, Reichenbach's principle implies that discriminating between common causes and causality is unprincipled since the discriminative results essentially depend on the selection of possible conditional variables. For some typical quantum cases, K. Reid et al. [Nat. Phys. 11, 414 (2015)] presented the statistic $C$ which can effectively discriminate quantum common causes and quantum causality over two quantum random variables (i.e., qubits) and which only uses measurement information about these two variables. In this paper, we formalize general quantum common causes and general quantum causality. Based on the formal representation, we further investigate their decidability via the statistic $C$ in general quantum cases. We demonstrate that (i) $C\ensuremath{\in}\left[\ensuremath{-}1,\frac{1}{27}\right]$ if two qubits are influenced by quantum common causes; (ii) $C\ensuremath{\in}\left[\ensuremath{-}\frac{1}{27},1\right]$ if the relation between two qubits is quantum causality; (iii) a geometric picture can illuminate the geometric interpretation of the probabilistic mixture of quantum common causes and quantum causality. This geometric picture also provides a basic heuristic to develop more complete methods for discriminating the cases corresponding to $C\ensuremath{\in}\left[\ensuremath{-}\frac{1}{27},\frac{1}{27}\right]$. Our results demonstrate that quantum common causes and quantum causality can be discriminated in a considerable scope.

arXiv:1806.10048•Physical Review A•Jun 26, 2018•10 citations

Efficient Distinction between Quantum Direct and Common Causes and its Experimental Verification

Feixiang Xu, Jiayi Lin, Ben Wang +4 more

Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal inference for certain cases, an effective and efficient way to detect the more general quantum causal structures is still lacking. Here, we introduce a quantity named `Causal Determinant' to efficiently identify the quantum causal structures between two quantum systems and experimentally verify the validity of the method. According to the causal determinant, the quantum direct cause imposed by an arbitrary unitary operator can be perfectly discriminated with the quantum common cause, in which the two quantum systems share a joint quantum state. In addition, the causal determinant has the capability to discriminate between more general causal structures and predict the range of their parameters. The ability to detect more general quantum causal structures of our method can shed new light on the field of quantum causal inference.

arXiv:2203.02752•Mar 5, 2022•0 citations

Quantum tests of causal structures and non-orthogonal states

Megan Agnew

This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. \n \nThe first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. \n \nThe second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters.

•Jun 13, 2014•0 citations
We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.
The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.
Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple subfields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation of Reichenbach's principle and enabling causal inference with only observational data. However, it is still not clear how quantum causal inference can provide operational advantages in general cases. Here, we have devised a photonic setup and experimentally realized an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario, thus revealing a universal quantum advantage in causal inference over its classical counterpart. We further demonstrate the explainability and stability of our causal discovery method, which is widely sought in data processing algorithms. Employing a fully observational approach, our result paves the way for studying quantum causality in general settings.
It has long been recognized as a difficult problem to determine whether the observed statistical correlations between two classical variables arise from causality or from common causes. Recent research has shown that, in a quantum theoretical framework, the mechanisms of entanglement and quantum coherence provide advantages in tackling this problem. In some particular cases, quantum common causes and quantum causality can be effectively distinguished by using observations alone. However, these solutions do not apply to all cases. There still exist a large class of cases in which quantum common causes and quantum causality cannot be distinguished. In this paper, along the line of considering unitary transformation as causality in the quantum world, we formally show that quantum common causes and quantum causality are universally separable. Based on the analysis, we further provide a general method to discriminate the two.
In classic cases, Reichenbach's principle implies that discriminating between common causes and causality is unprincipled since the discriminative results essentially depend on the selection of possible conditional variables. For some typical quantum cases, K. Reid et al. [Nat. Phys. 11, 414 (2015)] presented the statistic CCC which can effectively discriminate quantum common causes and quantum causality over two quantum random variables (i.e., qubits) and which only uses measurement information about these two variables. In this paper, we formalize general quantum common causes and general quantum causality. Based on the formal representation, we further investigate their decidability via the statistic CCC in general quantum cases. We demonstrate that (i) $C\ensuremath{\in}\left[\ensuremath{-}1,\frac{1}{27}\right]$ if two qubits are influenced by quantum common causes; (ii) $C\ensuremath{\in}\left[\ensuremath{-}\frac{1}{27},1\right]$ if the relation between two qubits is quantum causality; (iii) a geometric picture can illuminate the geometric interpretation of the probabilistic mixture of quantum common causes and quantum causality. This geometric picture also provides a basic heuristic to develop more complete methods for discriminating the cases corresponding to $C\ensuremath{\in}\left[\ensuremath{-}\frac{1}{27},\frac{1}{27}\right]$. Our results demonstrate that quantum common causes and quantum causality can be discriminated in a considerable scope.
Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal inference for certain cases, an effective and efficient way to detect the more general quantum causal structures is still lacking. Here, we introduce a quantity named `Causal Determinant' to efficiently identify the quantum causal structures between two quantum systems and experimentally verify the validity of the method. According to the causal determinant, the quantum direct cause imposed by an arbitrary unitary operator can be perfectly discriminated with the quantum common cause, in which the two quantum systems share a joint quantum state. In addition, the causal determinant has the capability to discriminate between more general causal structures and predict the range of their parameters. The ability to detect more general quantum causal structures of our method can shed new light on the field of quantum causal inference.
This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. \n \nThe first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. \n \nThe second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters.