In contribution published in AIP Conference Proceedings, No. 1018 (p. 40-5) some discrepancies in Copenhagen quantum mechanics have been summarized and the arguments have been gathered why in the description of microscopic reality the hidden-variable theory should be preferred. It has been shown, too, that the earlier gap in physical descriptions of the microscopic and macroscopic worlds may be practically removed. All corresponding statements have been based on proofs that have been published earlier and reproduced in the given contribution only partially. In the present paper the whole approach will be explained more systematically. Some important points newly analyzed will be added.
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Luders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance re…
Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ``logical pre- and post-selection paradoxes'', bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent similarity, we show that such effects can occur in noncontextual hidden variable theories, provided measurements are allowed to disturb the values of the hidden variables.
Coherence as a resource for $N$-box and quantum pigeonhole paradoxes
INL – International Iberian Nanotechnology Laboratory（国际伊比利亚纳米技术实验室）；Institute of Theoretical Physics, Ulm University（乌尔姆大学理论物理研究所）；Center for Integrated Quantum Science and Technology (IQST)（集成量子科学与技术中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of computational and communicational tasks. Strong contextuality is an extremal form of contextuality desc…
Many features of single-partite quantum walks can be simulated by classical waves. However, it was recently experimentally shown that some temporal sequences of measurements on a quantum walker do not admit a classical description in terms of macro-realistic theories. Here, we extend this observation and present pre- and post-selection scenarios in quantum walks leading to logical paradoxes. Such paradoxes were recently shown to be equivalent to proofs of contextuality, therefore we provide an additional argument for non-classicality of a quantum walk model. The assumptions behind the claims o…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality/nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. The present work aims to build a bridge between these two concepts from what we call possibilistic p…
This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. These research areas are highly relevant for the foundations of physics as well as the development of quantum technologies. In the first part, focussing on causality, we develop techniques for using generalised entropies to analyse distinctions between classical and non-classical causal structures. We derive new properties of Tsallis entropies of systems that follow from the relevant causal structure, and apply these to obtain new necessary constraints for classical…
The classical methods used by recursion theory and formal logic to block paradoxes do not work in quantum information theory. Since quantum information can exist as a coherent superposition of the classical ``yes'' and ``no'' states, certain tasks which are not conceivable in the classical setting can be performed in the quantum setting. Classical logical inconsistencies do not arise, since there exist fixed point states of the diagonalization operator. In particular, closed timelike curves need not be eliminated in the quantum setting, since they would not lead to any paradoxical outcome cont…
This paper explores the consequences of denying the "emptiness of paths not taken," EPNT, premise of Bernstein, Greenberger, Horne, and Zeilinger (BGHZ) in their paper titled, Bell theorem without inequalities.[ ] Carrying out the negation of EPNT leads to the concept of a "shadow stream." Streams are essentially particle implementations of the paths in Feynman path-integrals, resulting in a simple and consistent extension of the standard axioms for quantum mechanics. The construct provides elegant resolutions of single- and multi-particle interference paradoxes. Moreover, combining the argume…
It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an ensemble average. It is further hypothesized that the Langevin time also paces the motion of particles through coordinate time and is equal to the coordinate time of the present hypersurface in the frame of the Hubble expansion. Despite having a preferred frame, special relativity continues to hold in this formulation as a dynamical symmetry due to the presum…
A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events
ETH Zurich（苏黎世联邦理工学院）；Université Grenoble Alpes, Inria（格勒诺布尔阿尔卑斯大学，法国国家信息与自动化研究所）；ENS Lyon, Inria, LIP（里昂高等师范学校，法国国家信息与自动化研究所）
In human consciousness perceptions are distinct or atomistic events despite being perceived by an apparently undivided inner observer. This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is taken as a typical example of a self-referential negation in the perception space of an undivided observer. The conception of self-referential paradoxes is a unique ability of the human mind still lacking an explanation on the basis of logic. It will be shown that both classical and quantum logics fail to resolve the paradox because of the particle-like (atomi…
It was recently argued that the pigeonhole principle, which states that if three pigeons are put into two pigeonholes then at least one pigeonhole must contain more than one pigeon, is violated in quantum systems [Y. Aharonov et al., PNAS 113, 532 (2016)]. An experimental verification of this effect was recently reported [M.-C. Chen et al., PNAS 116, 1549 (2019)]. In another recent experimental work, it was argued that two entities were observed to exchange properties without meeting each other [Z.-H. Liu et al., Nat. Commun. 11, 3006 (2020)]. Here we describe all these proposals and experimen…
Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure inherent to quantum mechanics, which is naturally described in the language of weak values, and which is accessible experimentally via weak measurements. Using as an illustration, a gedanken-experiment due to Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence between a) a pair of classically contradictory assertions about the locatio…
A ring resonator involves a scattering process where a part of the output is fed again into the input. The same formal structure is encountered in the problem of time travel in a neighborhood of a closed timelike curve (CTC). We know how to describe quantum optics of ring resonators, and the resulting description agrees with experiment. We can apply the same formal strategy to any looped quantum evolution, in particular to the time travel. The argument is in its essence a topological one and thus does not refer to any concrete geometry. It is shown that the resulting paradigm automatically rem…
Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous paradoxes, many scientists doubt their internal consistencies. However, these paradoxes can be resolved within the framework of the existing physics without the introduction of new laws. To clarify the paper for the inexperienced reader, we include certain necessary basic concepts of statistical physics and quantum mechanics in this paper without the use of …
We demonstrate that it is possible to simulate Bell violations using probabilistic methods. A quantum state corresponding to optical experiments that violate the Bell inequality is generated, demonstrating that these quantum paradoxes can indeed be simulated probabilistically. This provides an explicit counter-example to Feynman's claim that such classical simulations could not be carried out.
Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.
The basic question in the long-standing debate about free will (FW) is not whether FW can be demonstrated to exist nor even whether it exists, but instead how to define it scientifically. If FW is not dismissed as an illusion nor identified with a variety of unpredictability, then logical paradoxes arise that make FW elusive to define. We resolve these paradoxes through a model of FW, in which FW is a new causal primitive empowered to override physical causality under guidance. We develop a simple mathematical realization of this model, that when applied to quantum theory, suggests that the ex…
The purpose of this book is to explain Quantum Bayesianism ('QBism') to "people without easy access to mathematical formulas and equations" (4-5). Qbism is an interpretation of quantum mechanics that "doesn't meddle with the technical aspects of the theory [but instead] reinterprets the fundamental terms of the theory and gives them new meaning" (3). The most important motivation for QBism, enthusiastically stated on the book's cover, is that QBism provides "a way past quantum theory's paradoxes and puzzles" such that much of the weirdness associated with quantum theory "dissolves under the le…
We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell's inequalities, quantum d…
In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level, resolving such paradoxes induce radical benefits - from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary…
In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded using several physical qubits. For example, one possible two qubit encoding identifies $|0\rangle_L=|01\rangle$ and $|1\rangle_L=|10\rangle$. If during the final measurement a $|11\rangle$ or $|00\rangle$ is observed an error is declared and the run is not included in subsequent analysis. We provide codewords for a simple bit-flip encoding, a way to encode the …
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schrödinger evolution equation and to the energy level equation written for the positive probability distribution are discussed. Instead of the transition probability amplitude (Feynman path integral) a transition probability is introduced. A new formulation of the conventional quantum mechanics (without wave function and density matrix) based on the ``probability representation'' of quantum states is given. An equation for the propagator in the new formulat…
We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection through verification at high fidelity level, where the unsuccessful ones are discarded without recovery operation. Then, gate operations are implemented by transversal measurements on the prepared logical cluster states. The noise threshold is improved significantly by making the high fidelity preparation and transversal measurement. It is estimated to be about 3…
Perfect state transfer (PST) is discussed in the context of passive quantum networks with logical bus topology, where many logical nodes communicate using the same shared media, without any external control. The conditions under which, a number of point-to-point PST links may serve as building blocks for the design of such multi-node networks are investigated. The implications of our results are discussed in the context of various Hamiltonians that act on the entire network, and are capable of providing PST between the logical nodes of a prescribed set in a deterministic manner.
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have string-like logical operators, which make the codes non-self-correcting. We introduce a notion of "logical string segments" to avoid difficulties in defining one dimensional objects in discrete lattices. We prove that every string-like logical operator of our code can be deformed to a disjoint union of short segments, and each segment is in the stabilizer group. The code has surface-like…
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it…
Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of …
No causal paradoxes will occur if a preferred reference frame for tachyons propagation is assumed, and results of Bell's inequality experiments may be well explained without using any telepathyc effect. We can read G. Faraci's and others' results, Lettere al Nuovo Cimento, 15, 607-611 (1974), as a first quantitive indication on the tachyons preferred reference frame velocity with respect to the Earth, as well as on the tachyons velocity in their preferred reference frame. In order to experimentally prove this assumption's validity, Aspect-like experiments should be slightly modified.
Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the condition on the local particle dimension. The resulting code is well-defined when the local Hilbert space dimension is prime. These codes can be divided into two different classes: the local stabilizer generators are either symmetric or antisymmetric with respect to the inversion operation. These is a nontrivial correspondence between these two classes. For a…
According to an argument proposed by Stapp, Quantum Mechanics violates the Locality Principle if the two hypotheses of {\sl Free Choices} and {\sl No backward-in-time influence} are assumed to hold, without the need of introducing hidden variables or criteria of reality. We develop an approach that endows the new hypotheses with a logico-mathematical formulation which allow us to perform an analysis of Stapp's argument, based on ordinary, not counterfactual, logic. According to our results, the analyzed argument is not able to conclude that Quantum Mechanics violates the Locality Principle.
Parallel Logical Measurements via Quantum Code Surgery
University of Oxford（牛津大学）；Massachusetts Institute of Technology（麻省理工学院）；IBM Quantum, IBM Almaden Research Center（IBM量子，IBM阿尔马登研究中心）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM沃森研究中心）
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality from a structural point of view, in the setting of partial Boolean algebras introduced by Kochen and Specker in their seminal work. These contrast with traditional quantum logic à la Birkhoff and von Neumann in that operations such as conjunction and disjunction are partial, only being defined in the domain where they are physically meaningful. We study how …
Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using s…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls, especially for logical qubits that involve more physical qubits, whose error tolerance is effective in principle though, their experimental demonstration is still demanding. Thus, how to best simplify the needed control and manifest its full advantage has become the key to widespread applications of geometric quantum computation. Here we propose a new fast and robust…
