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Keywords = Bell state measurement

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16 pages, 1547 KiB  
Article
Two-Party Quantum Private Comparison with Pauli Operators
by Min Hou, Yue Wu and Shibin Zhang
Axioms 2025, 14(8), 549; https://doi.org/10.3390/axioms14080549 - 22 Jul 2025
Viewed by 159
Abstract
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell [...] Read more.
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
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14 pages, 1581 KiB  
Article
Multi-Party Controlled Semi-Quantum Dialogue Protocol Based on Hyperentangled Bell States
by Meng-Na Zhao, Ri-Gui Zhou and Yun-Hao Feng
Entropy 2025, 27(7), 666; https://doi.org/10.3390/e27070666 - 21 Jun 2025
Viewed by 295
Abstract
To solve the fundamental problem of excessive consumption of classical resources and the simultaneous security vulnerabilities in semi-quantum dialogue systems, a multi-party controlled semi-quantum dialogue protocol based on hyperentangled Bell states is proposed. A single controlling party is vulnerable to information compromise due [...] Read more.
To solve the fundamental problem of excessive consumption of classical resources and the simultaneous security vulnerabilities in semi-quantum dialogue systems, a multi-party controlled semi-quantum dialogue protocol based on hyperentangled Bell states is proposed. A single controlling party is vulnerable to information compromise due to tampering or betrayal; the multi-party controlled mechanism (Charlie1 to Charlien) in this protocol establishes a distributed trust model. It mandates collective authorization from all controlling parties, significantly enhancing its robust resilience against untrustworthy controllers or collusion attacks. The classical participant Bob uses an adaptive Huffman compression algorithm to provide a framework for information transmission. This encoding mechanism assigns values to each character by constructing a Huffman tree, generating optimal prefix codes that significantly optimize the storage space complexity for the classical participant. By integrating the “immediate measurement and transmission” mechanism into the multi-party controlled semi-quantum dialogue protocol and coupling it with Huffman compression coding technology, this framework enables classical parties to execute encoding and decoding operations. The security of this protocol is rigorously proven through information-theoretic analysis and shows that it is resistant to common attacks. Furthermore, even in the presence of malicious controlling parties, this protocol robustly safeguards secret information against theft. The efficiency analysis shows that the proposed protocol provides benefits such as high communication efficiency and lower resource consumption for classical participants. Full article
(This article belongs to the Section Quantum Information)
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13 pages, 1194 KiB  
Article
Quantum Privacy Comparison with Ry Rotation Operation
by Min Hou and Yue Wu
Mathematics 2025, 13(7), 1071; https://doi.org/10.3390/math13071071 - 25 Mar 2025
Cited by 1 | Viewed by 340
Abstract
This paper presents a novel quantum privacy comparison (QPC) protocol that employs Ry rotation operations to enable two participants to securely compare their binary secrets without disclosing the actual data to any party except for the comparison result. In this protocol, classical [...] Read more.
This paper presents a novel quantum privacy comparison (QPC) protocol that employs Ry rotation operations to enable two participants to securely compare their binary secrets without disclosing the actual data to any party except for the comparison result. In this protocol, classical bits 0 and 1 are encoded as rotation angles 0 and π, respectively, using the Ry rotation operation. The participants apply these rotations to quantum sequences received from a semi-honest third party (TP) and return the encoded sequences to the TP. The TP then performs quantum measurements to determine the comparison result and announces it to the participants, ensuring fairness and privacy throughout the process. By leveraging the principles of quantum mechanics, the protocol is resistant to various quantum attack strategies, providing robust security against both external adversaries and insider threats. The protocol utilizes Bell states as quantum resources, Ry rotation operations for encoding classical information, and quantum measurements to derive the comparison result, making it experimentally feasible with current quantum technologies. Simulations conducted on a quantum platform validate the protocol’s practicality. Furthermore, each Bell state is used to compare one bit of binary information, achieving a qubit efficiency of 50%. Full article
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12 pages, 234 KiB  
Article
Quantum Private Comparison Protocol with Cluster States
by Min Hou and Yue Wu
Axioms 2025, 14(1), 70; https://doi.org/10.3390/axioms14010070 - 19 Jan 2025
Cited by 1 | Viewed by 941
Abstract
In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest third party (TP), who strictly adheres to [...] Read more.
In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest third party (TP), who strictly adheres to the protocol without deviation or collusion with any participant. The TP facilitates the private comparison by enabling users to encode their information through bit-flip or phase-shift operators applied to the received quantum sequences. Once the information is encoded, the sequences are returned to the TP, who can derive the comparison results without accessing any details of the private information. This design ensures correctness, privacy, and fairness throughout the process. The QPC protocol is robust against both external threats and participant attacks due to the incorporation of the decoy-state method and quantum key distribution techniques. Additionally, the protocol employs unitary operations and Bell-basis measurements, enhancing its technical feasibility for practical implementation. Notably, the proposed protocol achieves a qubit efficiency of up to 50%. This efficiency, combined with its strong security features, establishes the QPC protocol as a promising solution for private information comparisons within the realm of quantum cryptography. Full article
(This article belongs to the Section Mathematical Physics)
15 pages, 726 KiB  
Article
W-Class States—Identification and Quantification of Bell-CHSH Inequalities’ Violation
by Joanna K. Kalaga, Wiesław Leoński and Jan Peřina
Entropy 2024, 26(12), 1107; https://doi.org/10.3390/e26121107 - 18 Dec 2024
Cited by 1 | Viewed by 1209
Abstract
We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values [...] Read more.
We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values of the negativity, parameterized by concurrence, for violating the Bell-CHSH inequality. Additionally, we derive the value ranges of the mixedness measure, parameterized by concurrence and negativity for the qubit–qubit mixed state, guaranteeing the violation and non-violation of the Bell-CHSH inequality. Full article
(This article belongs to the Special Issue Entropy in Classical and Quantum Information Theory with Applications)
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15 pages, 762 KiB  
Article
Practical Security of Continuous Variable Measurement- Device-Independent Quantum Key Distribution with Local Local Oscillator
by Yewei Guo, Hang Zhang and Ying Guo
Mathematics 2024, 12(23), 3732; https://doi.org/10.3390/math12233732 - 27 Nov 2024
Cited by 1 | Viewed by 931
Abstract
Continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) can remove the feasible side-channel attacks on detectors based on the accurate Bell-state measurement (BSM), where an optical amplitude modulator (AM) plays a crucial role in managing the intensity of the transmitted light pulse. However, [...] Read more.
Continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) can remove the feasible side-channel attacks on detectors based on the accurate Bell-state measurement (BSM), where an optical amplitude modulator (AM) plays a crucial role in managing the intensity of the transmitted light pulse. However, the AM-involved practical security has remained elusive as the operating frequency of the AM usually determines the actual secret key rate of the CV-MDI-QKD system. We find that an imperfect pulse generated from the AM at high speed can lead to a challenge to the practical security as a minor intensity change of the light pulse can bring about a potential information leakage. Taking advantage of this flaw, we suggest an attack strategy targeting the embedded AM in CV-MDI-QKD without sending the local oscillator (LO). This attack can damage the AM and thus decrease the estimated secret key rate of the system even when the orthogonal local LO (LLO) scheme is carried out. To assess the practical security risk resulting from the leaked information from the AM, we conduct numerical simulations to demonstrate the influence of the AM on the CVMDI-QKD system. Full article
(This article belongs to the Special Issue Quantum Cryptography and Applications)
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17 pages, 647 KiB  
Article
Deriving Three-Outcome Permutationally Invariant Bell Inequalities
by Albert Aloy, Guillem Müller-Rigat, Jordi Tura and Matteo Fadel
Entropy 2024, 26(10), 816; https://doi.org/10.3390/e26100816 - 25 Sep 2024
Cited by 2 | Viewed by 1138
Abstract
We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with N observers, each of which performs one out of two possible three-outcome measurements on their share of the system. [...] Read more.
We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with N observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower-dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of N. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles. Full article
(This article belongs to the Special Issue Quantum Correlations in Many-Body Systems)
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11 pages, 1723 KiB  
Article
Research on Intraparticle to Interparticle Entanglement Swapping Protocols
by Jiangmei Tang, Shaomeng Wang, Bingyang Liang and Yubin Gong
Appl. Sci. 2024, 14(17), 8035; https://doi.org/10.3390/app14178035 - 8 Sep 2024
Viewed by 919
Abstract
Entanglement is one of the most striking features of quantum systems, whereby its non-classical correlation is an essential resource in numerous quantum protocols. Entanglement can be divided into two categories: interparticle and intraparticle entanglement. There are both distinctions and similarities between these two [...] Read more.
Entanglement is one of the most striking features of quantum systems, whereby its non-classical correlation is an essential resource in numerous quantum protocols. Entanglement can be divided into two categories: interparticle and intraparticle entanglement. There are both distinctions and similarities between these two kinds of entangled states. This work delves into these distinctions and similarities from the following aspects: correlation and non-locality, robustness, the mechanisms of generation and separation, and practical applications. Entanglement swapping is a technique based on quantum entanglement. As entanglement has different categories, entanglement swapping also has various types, including interparticle to interparticle and intraparticle to interparticle. Swapping protocols from intraparticle entanglement to interparticle entanglement can be applied to super quantum dense encoding, quantum information transmission, quantum teleportation, etc. Thus, this work proposes three swapping protocols, from spin–orbit intraparticle entanglement to spin–spin interparticle entanglement, based on Bell state joint measurement, the cross-Kerr medium, and linear optical elements. This work can help us better understand entanglement by analyzing the differences and similarities between the two types of entangled states. It can also enhance entanglement swapping protocols, from spin–orbit intraparticle to spin–spin interparticle entanglement, for use in quantum information transfer. Full article
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9 pages, 2083 KiB  
Article
A Hybrid Metadetector for Measuring Bell States of Optical Angular Momentum Entanglement
by Yang Ming
Sensors 2024, 24(15), 4817; https://doi.org/10.3390/s24154817 - 25 Jul 2024
Viewed by 1000
Abstract
High-dimensional entanglement of optical angular momentum has shown its enormous potential for increasing robustness and data capacity in quantum communication and information multiplexing, thus offering promising perspectives for quantum information science. To make better use of optical angular momentum entangled states, it is [...] Read more.
High-dimensional entanglement of optical angular momentum has shown its enormous potential for increasing robustness and data capacity in quantum communication and information multiplexing, thus offering promising perspectives for quantum information science. To make better use of optical angular momentum entangled states, it is necessary to develop a reliable platform for measuring and analyzing them. Here, we propose a hybrid metadetector of monolayer transition metal dichalcogenide (TMD) integrated with spin Hall nanoantenna arrays for identifying Bell states of optical angular momentum. The corresponding states are converted into path-entangled states of propagative polaritonic modes for detection. Several Bell states in different forms are shown to be identified effectively. TMDs have emerged as an attractive platform for the next generation of on-chip optoelectronic devices. Our work may open up a new horizon for devising integrated quantum circuits based on these two-dimensional van der Waals materials. Full article
(This article belongs to the Section Optical Sensors)
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19 pages, 731 KiB  
Article
Correlations in the EPR State Observables
by Daniel F. Orsini, Luna R. N. Oliveira and Marcos G. E. da Luz
Entropy 2024, 26(6), 476; https://doi.org/10.3390/e26060476 - 30 May 2024
Viewed by 1396
Abstract
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of [...] Read more.
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of observables describing the composite are equally probable upon measurement, and (b) The absence of concurrence (positive reinforcement) between any of the observables within a particular system; implying that their associated operators do not commute. The so-called EPR states are known to observe (a). Here, we demonstrate in very general (but straightforward) terms that they also satisfy condition (b), a relevant technical fact often overlooked. As an illustration, we work out in detail the three-level systems, i.e., qutrits. Furthermore, given the special characteristics of EPR states (such as maximal entanglement, among others), one might intuitively expect the CHSH correlation, computed exclusively for the observables of qubit EPR states, to yield values greater than two, thereby violating Bell’s inequality. We show such a prediction does not hold true. In fact, the combined properties of (a) and (b) lead to a more limited range of values for the CHSH measure, not surpassing the nonlocality threshold of two. The present constitutes an instructive example of the subtleties of quantum correlations. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
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14 pages, 323 KiB  
Article
Does Quantum Mechanics Require “Conspiracy”?
by Ovidiu Cristinel Stoica
Entropy 2024, 26(5), 411; https://doi.org/10.3390/e26050411 - 9 May 2024
Cited by 8 | Viewed by 1544
Abstract
Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an [...] Read more.
Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis. Full article
(This article belongs to the Section Quantum Information)
17 pages, 578 KiB  
Review
Quantum Nonlocality: How Does Nature Do It?
by Marian Kupczynski
Entropy 2024, 26(3), 191; https://doi.org/10.3390/e26030191 - 23 Feb 2024
Cited by 8 | Viewed by 3119
Abstract
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality [...] Read more.
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other’s state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell–CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter’s freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole. Full article
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19 pages, 624 KiB  
Article
Superdeterminism without Conspiracy
by Tim Palmer
Universe 2024, 10(1), 47; https://doi.org/10.3390/universe10010047 - 18 Jan 2024
Cited by 3 | Viewed by 2204
Abstract
Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial [...] Read more.
Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics. Full article
(This article belongs to the Special Issue Approaches towards Quantum Foundations)
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12 pages, 1606 KiB  
Article
Events with Different Emotional Valence Affect the Eye’s Lacrimal Caruncle Temperature Changes in Sheep
by Marta Comin, Elie Atallah, Matteo Chincarini, Silvia Michela Mazzola, Elisabetta Canali, Michela Minero, Bruno Cozzi, Emanuela Rossi, Giorgio Vignola and Emanuela Dalla Costa
Animals 2024, 14(1), 50; https://doi.org/10.3390/ani14010050 - 22 Dec 2023
Cited by 2 | Viewed by 2179
Abstract
Infrared thermography (IRT) has been recently applied to measure lacrimal caruncle temperature non-invasively since this region is related to the sympathetic response, and it seems a promising technique that is able to infer negative emotions in sheep (e.g., fear). However, the scientific literature [...] Read more.
Infrared thermography (IRT) has been recently applied to measure lacrimal caruncle temperature non-invasively since this region is related to the sympathetic response, and it seems a promising technique that is able to infer negative emotions in sheep (e.g., fear). However, the scientific literature so far is limited in understanding whether a caruncle’s temperature changes also in response to positive emotional states in sheep. Through classical conditioning, we aimed to assess how a positive or a negative event affects the physiological (lacrimal caruncle temperature measured with IRT and cortisol levels) and behavioral responses of sheep (ear position). Fourteen ewes from the same flock were randomly assigned to two treatment groups: positive (n = 7) and negative (n = 7). Each group was then trained through classical conditioning to associate a neutral auditory (ring bell) stimulus to an oncoming event: for the positive group, the presence of a food reward (maize grains), while for the negative one, the opening of an umbrella. After three weeks of training, before (at rest) and after (post-treatment), lacrimal caruncle temperature was non-invasively measured via IRT, and saliva samples were gently collected to measure cortisol levels. During treatment, sheep behavior was videorecorded and then analyzed using a focal animal sampling technique. At rest, the eye’s lacrimal caruncle temperature was similar in both groups, while post-treatment, a significant increase was shown only in the negative group (t-test; p = 0.017). In the anticipation phase, sheep in the positive group kept their ears forward longer compared to those in the negative one (Mann–Whitney; p < 0.014), 8.3 ± 2.1 s and 5.2 ± 4.2 s, respectively. The behavioral response observed reflects a learnt association between a neutral stimulus and events with different emotional valence. Cortisol concentration slightly increased in both groups post-treatment. Our results confirm that IRT is a non-invasive technique that can be useful when applied to assess how positive and negative events may affect the physiological response in sheep. Full article
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33 pages, 4382 KiB  
Article
Weak versus Deterministic Macroscopic Realism, and Einstein–Podolsky–Rosen’s Elements of Reality
by Jesse Fulton, Manushan Thenabadu, Run Yan Teh and Margaret D. Reid
Entropy 2024, 26(1), 11; https://doi.org/10.3390/e26010011 - 21 Dec 2023
Cited by 9 | Viewed by 2279
Abstract
The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of [...] Read more.
The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory. Full article
(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)
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