scholarly journals The Operational Choi–Jamiołkowski Isomorphism

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1063 ◽  
Author(s):  
Emily Adlam
Keyword(s):  
Quantum Mechanics ◽  
Causal Structure ◽  
Temporal Correlations ◽  
Fundamental Object ◽  
Generalized Probabilistic Theories ◽  
Operational Theory ◽  
Local Correlations ◽  
Non Local ◽  
Operational Formulation ◽  
Probabilistic Theories

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.

scholarly journals Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations

2017 ◽  
Vol 56 (10) ◽  
pp. 3323-3339 ◽  
Author(s):  
Ricardo Gallego Torromé
Keyword(s):  
Quantum Mechanics ◽  
Local Correlations ◽  
Non Local ◽  
Emergent Quantum Mechanics

scholarly journals Causation does not explain contextuality

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 63 ◽  
Author(s):  
Sally Shrapnel ◽  
Fabio Costa
Keyword(s):  
Quantum Mechanics ◽  
Causal Structure ◽  
Quantum Correlations ◽  
Global Constraints ◽  
Local Constraints ◽  
The Past ◽  
Interpretations Of Quantum Mechanics ◽  
The World ◽  
Non Local ◽  
Initial States

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

scholarly journals Relaxed uncertainty relations and information processing

2009 ◽  
Vol 9 (9&10) ◽  
pp. 801-832 ◽  
Author(s):  
G. Ver Steeg ◽  
S. Wehner
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Random Access ◽  
The Other ◽  
Uncertainty Relations ◽  
Expectation Values ◽  
Chsh Inequality ◽  
Local Correlations ◽  
Non Local

We consider a range of "theories'' that violate the uncertainty relation for anti-commuting observables derived. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to construct a hierarchy of related non-signaling theories, and show that on one hand they admit superstrong random access encodings and exponential savings for a particular communication problem, while on the other hand it becomes much harder in these theories to learn a state. We show that the existence of these effects stems from the absence of certain constraints on the expectation values of commuting measurements from our non-signaling theories that are present in quantum theory.

scholarly journals Generalized Probabilistic Theories in a New Light

2021 ◽  
Author(s):  
Raed Shaiia
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Mechanical ◽  
Infinite Dimensional ◽  
Classical Systems ◽  
Generalized Probabilistic Theories ◽  
Deterministic Description ◽  
New Formulation ◽  
The Universe ◽  
Probabilistic Theories

Abstract In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, and give the guidelines to how to extend this work to infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call extended operational-probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell’s theorem, and at the same time solves the measurement problem. This is why we will see that the question of why our universe is quantum mechanical rather than classical is misplaced. The only difference that exists between a classical universe and a quantum mechanical one lies merely in which observables are compatible and which are not. Besides, this extended probability theory which we present in this paper shows that it is non-determinacy, or to be more precise, the non-deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows us that what used to be considered as purely classical systems and to be treated that way are in fact able to be manipulated according to the rules of quantum mechanics –with this new understanding of these rules- and that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition to all that, this paper shows that without the use of complex vector spaces, we cannot have any kind of continuous evolution of the states of any system.

scholarly journals On quantum entanglement, counterfactuals, causality and dispositions

Synthese ◽  
2017 ◽  
Vol 197 (10) ◽  
pp. 4161-4185
Author(s):  
Tomasz Bigaj
Keyword(s):  
Quantum Mechanics ◽  
Entangled States ◽  
Causal Mechanism ◽  
Interpretation Of Quantum Mechanics ◽  
Counterfactual Conditionals ◽  
Local Character ◽  
Causal Connections ◽  
Local Correlations ◽  
Non Local ◽  
Counterfactual Approach

Abstract The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them.

scholarly journals Implications of superstrong non-locality for cryptography

2006 ◽  
Vol 462 (2071) ◽  
pp. 1919-1932 ◽  
Author(s):  
Harry Buhrman ◽  
Matthias Christandl ◽  
Falk Unger ◽  
Stephanie Wehner ◽  
Andreas Winter
Keyword(s):  
Quantum Mechanics ◽  
Oblivious Transfer ◽  
Secure Computation ◽  
Bit Commitment ◽  
Local Correlations ◽  
Non Local ◽  
Non Locality

Non-local boxes are hypothetical ‘machines’ that give rise to superstrong non-local correlations, leading to a stronger violation of Bell/Clauser, Horne, Shimony & Holt inequalities than is possible within the framework of quantum mechanics. We show how non-local boxes can be used to perform any two-party secure computation. We first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non-local boxes. Both have been shown to be impossible using quantum mechanics alone.

scholarly journals Quantum Mechanics Interpretation on Planck Scale

2020 ◽  
Vol 65 (1) ◽  
pp. 17
Author(s):  
I. Licata
Keyword(s):  
Quantum Mechanics ◽  
Standard Model ◽  
Particle Physics ◽  
Planck Scale ◽  
Beyond The Standard Model ◽  
Interpretation Of Quantum Mechanics ◽  
Vacuum Model ◽  
The Standard Model ◽  
Local Correlations ◽  
Non Local

In the last years, many different primeval quantization theories on the Planck scale have been developed. Their goal is to provide a vacuum model able to ground the research beyond the Standard Model. Despite their goal is quite ambitious and aims toward particle physics, a necessary and notable consequence is we can read Quantum Mechanics from an emergent viewpoint. Different hypotheses on elementary cells are possible. We will focus here on the conceptual features of G. ’t Hooft and F.Winterberg theories with a special attention for the emerging of non-local correlations. These theories define a new style in the interpretation of Quantum Mechanics.

scholarly journals Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 114
Author(s):  
Michael Silberstein ◽  
William Mark Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Causal Explanation ◽  
Causal Structure ◽  
Minkowski Spacetime ◽  
Physical Principle ◽  
Causal Principle ◽  
Complete Rejection ◽  
Epr Correlations ◽  
Tsirelson Bound

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.

Is Quantum Mechanics Non-Local?

2002 ◽  
pp. 125-136 ◽  
Author(s):  
William G. Unruh
Keyword(s):  
Quantum Mechanics ◽  
Non Local
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