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Pusey-Barrett-Rudolph theorem under noisy channels

Andrés F. Ducuara, Cristian E. Susa, John Henry Reina

Published Aug 17, 2016• 1 citation
OpenAlex

Abstract

The Pusey-Barrett-Rudolph (PBR) theorem deals with the realism of the quantum state. It establishes that every pure quantum state is real, in the context of $\psi$-ontic quantum ontological models. In order to achieve this, PBR consider an ad hoc postulate termed the Preparation Independence Postulate (PIP). Here we argue that even without the use of the PIP, the PBR argument leads to a link between scalability and realism of quantum states whereby the latter can be achieved through the former. Further, we consider a set of n-qubit registers in interaction with an environment by means of i) individual and ii) collective couplings. In both cases, we analytically show that the phenomenon of achieving realism through scalability is still present, even though this now occurs at a slower rate. Searching for an optimisation of this phenomenon, we report numerical experiments up to n = 4 qubits: for individual qubit-noise coupling, be it a bit, a phase, or a bit-phase flip noise, the numerical search exhibits the same response to all the different noisy channels, without improving the analytical expectation. In contrast, the collective qubit-noise coupling leads to a more efficient display of the phenomenon, and a variety of noise channel-dependent behaviours emerge.

Related papers

Not-Post-Peierls compatibility under noisy channels

Andrés F. Ducuara, Cristian E. Susa, John Henry Reina

Abstract The Pusey–Barrett–Rudolph (PBR) theorem deals with the realism of the quantum states. It establishes that every pure quantum state is real, in the context of quantum ontological models. Specifically, by guaranteeing the property of not-Post-Peierls ( ¬ PP) compatibility (or antidistinguishability) for a particular set of states P , together with the ad hoc postulate known as preparation independence postulate (PIP), the theorem establishes that these two properties imply the ψ -onticity (realism) of the set of all pure states. This PBR result has triggered two particular lines of research: On the one hand, it has been possible to derive similar results without the use of the PIP, although at the expense of implying weaker properties than ψ -onticity. On the other hand, it has also been proven that the property of ¬ PP compatibility alone is an explicit witness of usefulness for the task known as conclusive exclusion of states. In this work, we explore the ¬ PP compatibility of the set of states P , when P is under the interaction of some noisy channels, which would consequently let us identify some noisy scenarios where it is still possible to perform the task of conclusive exclusion of states. Specifically, we consider the set P of n -qubit states in interaction with an environment by means of (i) individual and (ii) collective couplings. In both cases, we analytically show that the phenomenon of achieving ¬ PP compatibility, although reduced, it is still present. Searching for an optimisation of this phenomenon, we report numerical experiments up to n = 4 qubits. For individual qubit-noise coupling, be it a bit, a phase, or a bit–phase flip noise, the numerical search exhibits the same response to all the different noisy channels, without improving the analytical expectation. In contrast, the collective qubit-noise coupling leads to a more efficient numerical display of the phenomenon, and a variety of noise channel-dependent behaviours emerge. Furthermore, by adopting a slight modification of the definition of ψ -onticity, from being a property exclusively of sets of pure states to be a property of general sets of states (now ρ -onticity), in particular of the considered noisy set P , our results can also be seen as addressing the ρ -ontic realism of the set of n -qubit states P under the considered noisy channels.

arXiv:1608.05034•Journal of Physics A Mathematical and Theoretical•May 15, 2017•3 citations

From Joint to Single-System Psi-Onticity Without Preparation Independence

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The Pusey-Barrett-Rudolph (PBR) theorem establishes $ψ$-onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of $ψ$-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes $ψ$-onticity for composite systems prepared in product states, the $ψ$-onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving $ψ$-epistemic models, and strengthens the conceptual foundations of $ψ$-ontology.

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Reality of the quantum state: Towards a stronger ψ -ontology theorem

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The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out $\ensuremath{\psi}$-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit $\ensuremath{\psi}$-epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of $\ensuremath{\psi}$ epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.

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The Pusey--Barrett--Rudolph (PBR) theorem is commonly taken to establish that a pure quantum state represents a physical property of the system to which it is assigned, rather than merely encoding knowledge. In this work, I distinguish between state-first and dynamics-first physical theories, and argue that this reading presupposes the former. These two types of theories support different approaches to causal explanation, and one of PBR's stated assumptions depends on the state-first approach. Using a recent interpretation of quantum theory as a concrete example, I show how a dynamics-first theory can explain the PBR correlations while maintaining a broadly epistemic reading of quantum states. I conclude that the PBR theorem supports a dilemma: either the quantum state is part of reality, or reality is not fundamentally built out of states.

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Detection-efficiency loophole and the Pusey-Barrett-Rudolph theorem

Arijit Dutta, Marcin Pawłowski, Marek Żukowski

The detection-efficiency loophole poses a significant problem for experimental tests of Bell inequalities. The recently discovered Pusey-Barrett-Rudolph (PBR) theorem suffers from the same vulnerability. In this paper we calculate the critical detection efficiency, below which the PBR argument for the ontic nature of quantum state is inconclusive. This is done for the maximally $\ensuremath{\psi}$-epistemic models. We use two different definitions of this property. The optimal number of parties for which the critical detection efficiency is the lowest is given. We also approach the problem from the opposite direction. We provide a function that enables us to specify which epistemic models are ruled out by the results of an experiment with a given detection efficiency.

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Is the Quantum State Real? An Extended Review of ψ-Ontology Theorems

Matthew Leifer

Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.

arXiv:1409.1570•Quanta•Nov 5, 2014•306 citations
The Pusey-Barrett-Rudolph (PBR) theorem deals with the realism of the quantum state. It establishes that every pure quantum state is real, in the context of ψ\psiψ-ontic quantum ontological models. In order to achieve this, PBR consider an ad hoc postulate termed the Preparation Independence Postulate (PIP). Here we argue that even without the use of the PIP, the PBR argument leads to a link between scalability and realism of quantum states whereby the latter can be achieved through the former. Further, we consider a set of n-qubit registers in interaction with an environment by means of i) individual and ii) collective couplings. In both cases, we analytically show that the phenomenon of achieving realism through scalability is still present, even though this now occurs at a slower rate. Searching for an optimisation of this phenomenon, we report numerical experiments up to n = 4 qubits: for individual qubit-noise coupling, be it a bit, a phase, or a bit-phase flip noise, the numerical search exhibits the same response to all the different noisy channels, without improving the analytical expectation. In contrast, the collective qubit-noise coupling leads to a more efficient display of the phenomenon, and a variety of noise channel-dependent behaviours emerge.
Abstract The Pusey–Barrett–Rudolph (PBR) theorem deals with the realism of the quantum states. It establishes that every pure quantum state is real, in the context of quantum ontological models. Specifically, by guaranteeing the property of not-Post-Peierls ( ¬ PP) compatibility (or antidistinguishability) for a particular set of states P , together with the ad hoc postulate known as preparation independence postulate (PIP), the theorem establishes that these two properties imply the ψ -onticity (realism) of the set of all pure states. This PBR result has triggered two particular lines of research: On the one hand, it has been possible to derive similar results without the use of the PIP, although at the expense of implying weaker properties than ψ -onticity. On the other hand, it has also been proven that the property of ¬ PP compatibility alone is an explicit witness of usefulness for the task known as conclusive exclusion of states. In this work, we explore the ¬ PP compatibility of the set of states P , when P is under the interaction of some noisy channels, which would consequently let us identify some noisy scenarios where it is still possible to perform the task of conclusive exclusion of states. Specifically, we consider the set P of n -qubit states in interaction with an environment by means of (i) individual and (ii) collective couplings. In both cases, we analytically show that the phenomenon of achieving ¬ PP compatibility, although reduced, it is still present. Searching for an optimisation of this phenomenon, we report numerical experiments up to n = 4 qubits. For individual qubit-noise coupling, be it a bit, a phase, or a bit–phase flip noise, the numerical search exhibits the same response to all the different noisy channels, without improving the analytical expectation. In contrast, the collective qubit-noise coupling leads to a more efficient numerical display of the phenomenon, and a variety of noise channel-dependent behaviours emerge. Furthermore, by adopting a slight modification of the definition of ψ -onticity, from being a property exclusively of sets of pure states to be a property of general sets of states (now ρ -onticity), in particular of the considered noisy set P , our results can also be seen as addressing the ρ -ontic realism of the set of n -qubit states P under the considered noisy channels.
The Pusey-Barrett-Rudolph (PBR) theorem establishes ψψψ-onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of ψψψ-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes ψψψ-onticity for composite systems prepared in product states, the ψψψ-onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving ψψψ-epistemic models, and strengthens the conceptual foundations of ψψψ-ontology.
The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out $\ensuremath{\psi}$-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit $\ensuremath{\psi}$-epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of $\ensuremath{\psi}$ epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.
The Pusey--Barrett--Rudolph (PBR) theorem is commonly taken to establish that a pure quantum state represents a physical property of the system to which it is assigned, rather than merely encoding knowledge. In this work, I distinguish between state-first and dynamics-first physical theories, and argue that this reading presupposes the former. These two types of theories support different approaches to causal explanation, and one of PBR's stated assumptions depends on the state-first approach. Using a recent interpretation of quantum theory as a concrete example, I show how a dynamics-first theory can explain the PBR correlations while maintaining a broadly epistemic reading of quantum states. I conclude that the PBR theorem supports a dilemma: either the quantum state is part of reality, or reality is not fundamentally built out of states.
The detection-efficiency loophole poses a significant problem for experimental tests of Bell inequalities. The recently discovered Pusey-Barrett-Rudolph (PBR) theorem suffers from the same vulnerability. In this paper we calculate the critical detection efficiency, below which the PBR argument for the ontic nature of quantum state is inconclusive. This is done for the maximally $\ensuremath{\psi}$-epistemic models. We use two different definitions of this property. The optimal number of parties for which the critical detection efficiency is the lowest is given. We also approach the problem from the opposite direction. We provide a function that enables us to specify which epistemic models are ruled out by the results of an experiment with a given detection efficiency.
Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.