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Articles 1 - 30 of 197
Full-Text Articles in Physics
Toward Local Madelung Mechanics In Spacetime, Mordecai Waegell
Toward Local Madelung Mechanics In Spacetime, Mordecai Waegell
Mathematics, Physics, and Computer Science Faculty Articles and Research
It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating …
Instability And Quantization In Quantum Hydrodynamics, Yakir Aharonov, Tomer Shushi
Instability And Quantization In Quantum Hydrodynamics, Yakir Aharonov, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how the quantum hydrodynamical formulation of quantum mechanics converts the nonlocality in the standard wave-like description of quantum systems by an instability of the quantum system, which opens the door to a new way for studying quantum systems based on known methodologies for studying the stability of fluids. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.
Comment On “Photons Can Tell ‘Contradictory’ Answer About Where They Have Been”, Gregory Reznick, Carlotta Versmold, Jan Dziewior, Florian Huber, Harald Weinfurter, Justin Dressel, Lev Vaidman
Comment On “Photons Can Tell ‘Contradictory’ Answer About Where They Have Been”, Gregory Reznick, Carlotta Versmold, Jan Dziewior, Florian Huber, Harald Weinfurter, Justin Dressel, Lev Vaidman
Mathematics, Physics, and Computer Science Faculty Articles and Research
Yuan and Feng (Eur. Phys. J. Plus 138:70, 2023) recently proposed a modification of the nested Mach–Zehnder interferometer experiment performed by Danan et al. (Phys. Rev. Lett. 111:240402, 2013) and argued that photons give “contradictory” answers about where they have been, when traces are locally imprinted on them in different ways. They concluded that their results are comprehensible from what they call the “three-path interference viewpoint,” but difficult to explain from the “discontinuous trajectory” viewpoint advocated by Danan et al. We argue that the weak trace approach (the basis of the “discontinuous trajectory” viewpoint) provides a consistent explanation of the …
Improving The Proof Of The Born Rule Using A Physical Requirement On The Dynamics Of Quantum Particles, Yakir Aharonov, Tomer Shushi
Improving The Proof Of The Born Rule Using A Physical Requirement On The Dynamics Of Quantum Particles, Yakir Aharonov, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time Δt between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to produce the Born rule in its explicit form by improving the result given in [1]. While the proposed postulate is still not part of the quantum mechanics postulates, every experiment obeys it, and it cannot be deduced using the standard postulates of quantum mechanics.
Gaussian Rbf Kernels Via Fock Spaces: Quaternionic And Several Complex Variables Settings, Antonino De Martino, Kamal Diki
Gaussian Rbf Kernels Via Fock Spaces: Quaternionic And Several Complex Variables Settings, Antonino De Martino, Kamal Diki
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternionic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.
Stabilizing Two-Qubit Entanglement With Dynamically Decoupled Active Feedback, Sacha Greenfield, Leigh Martin, Felix Motzoi, K. Birgitta Whaley, Justin Dressel, Eli M. Levenson-Falk
Stabilizing Two-Qubit Entanglement With Dynamically Decoupled Active Feedback, Sacha Greenfield, Leigh Martin, Felix Motzoi, K. Birgitta Whaley, Justin Dressel, Eli M. Levenson-Falk
Mathematics, Physics, and Computer Science Faculty Articles and Research
We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f-distributed qubit-frequency noise, and relaxation. We …
Programmable Heisenberg Interactions Between Floquet Qubits, Long B. Nguyen, Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Bibek Bhandari, Debmalya Das, Ravi K. Naik, John Mark Kreikebaum, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi
Programmable Heisenberg Interactions Between Floquet Qubits, Long B. Nguyen, Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Bibek Bhandari, Debmalya Das, Ravi K. Naik, John Mark Kreikebaum, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi
Mathematics, Physics, and Computer Science Faculty Articles and Research
The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate …
What Does ‘(Non)-Absoluteness Of Observed Events’ Mean?, Emily Adlam
What Does ‘(Non)-Absoluteness Of Observed Events’ Mean?, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
Recently there have emerged an assortment of theorems relating to the ‘absoluteness of emerged events,’ and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical non-absoluteness, such as relationalism or perspectivalism. However, in our view a close examination of these theorems fails to convincingly support such possibilities. In this paper we argue that the Wigner’s friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all best understood as demonstrating that if quantum mechanics is universal, and if certain auxiliary assumptions hold, then the world …
Weak Measurements And Quantum-To-Classical Transitions In Free Electron–Photon Interactions, Yiming Pan, Eliahu Cohen, Ebrahim Karimi, Avraham Gover, Norbert Schönenberger, Tomáš Chlouba, Kangpeng Wang, Saar Nehemia, Peter Hommelhoff, Ido Kaminer, Yakir Aharonov
Weak Measurements And Quantum-To-Classical Transitions In Free Electron–Photon Interactions, Yiming Pan, Eliahu Cohen, Ebrahim Karimi, Avraham Gover, Norbert Schönenberger, Tomáš Chlouba, Kangpeng Wang, Saar Nehemia, Peter Hommelhoff, Ido Kaminer, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron–photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light–matter interactions and show that any classical electron-laserbeam interaction can be represented as an outcome of weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, exp(-Γ2/2) , quantifies the …
Aspects Of The Phenomenology Of Interference That Are Genuinely Nonclassical, Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
Aspects Of The Phenomenology Of Interference That Are Genuinely Nonclassical, Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
Mathematics, Physics, and Computer Science Faculty Articles and Research
Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al., arXiv:2111.13727]. This raises the question of what other aspects of the phenomenology of interference do in fact resist classical explanation. We answer this question by demonstrating that the most basic quantum wave-particle duality relation, which expresses the precise tradeoff between path distinguishability and fringe visibility, cannot be reproduced in any noncontextual model. We do this by …
Entangled Photon Anti-Correlations Are Evident From Classical Electromagnetism, Ken Wharton, Emily Adlam
Entangled Photon Anti-Correlations Are Evident From Classical Electromagnetism, Ken Wharton, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
For any experiment with two entangled photons, some joint measurement outcomes can have zero probability for a precise choice of basis. These perfect anti-correlations would seem to be a purely quantum phenomenon. It is, therefore, surprising that these very anti-correlations are also evident when the input to the same experiment is analyzed via classical electromagnetic theory. Demonstrating this quantum–classical connection for arbitrary two-photon states and analyzing why it is successful motivates alternative perspectives concerning entanglement, the path integral, and other topics in quantum foundations.
Quantum Reality With Negative-Mass Particles, Mordecai Waegell, Eliahu Cohen, Avshalom C. Elitzur, Jeff Tollaksen, Yakir Aharonov
Quantum Reality With Negative-Mass Particles, Mordecai Waegell, Eliahu Cohen, Avshalom C. Elitzur, Jeff Tollaksen, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top–down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to …
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a recent paper, [Y. Aharonov, S. Popescu, D. Rohrlich, Proc. Natl. Acad. Sci. U.S.A.118 e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and …
Quantum Stirling Heat Engine Operating In Finite Time, Debmalya Das, George Thomas, Andrew N. Jordan
Quantum Stirling Heat Engine Operating In Finite Time, Debmalya Das, George Thomas, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that …
Aharonov–Bohm Effect With An Effective Complex-Valued Vector Potential, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell
Aharonov–Bohm Effect With An Effective Complex-Valued Vector Potential, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell
Mathematics, Physics, and Computer Science Faculty Articles and Research
The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov–Bohm (AB) scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the AB phase before the source is fully encircled. While this does not necessarily change the nonlocal status of the AB effect, it brings new insights into it. Moreover, we discuss how these results might have consequences for the correspondence principle, making complex vector potentials relevant to the study of classical …
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, I show how the Aharonov–Vaidman identity A|ψ>=<A⟩|ψ>+ΔA| ψ⊥A> can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation ΔAΔB≥12|< [A,B]>| than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations …
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix programme has correctly identified a notion of ‘causal order’ which plays an important role in fundamental physics, but this notion is weaker than the common-sense conception of causation because it does not involve asymmetry. We argue that causal order plays an important role in grounding more familiar causal phenomena. Then we apply these conclusions to the causal modelling programme within quantum foundations, …
The Temporal Asymmetry Of Influence Is Not Statistical, Emily Adlam
The Temporal Asymmetry Of Influence Is Not Statistical, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
We argue that the temporal asymmetry of influence is not merely the result of thermodynamics: it is a consequence of the fact that modal structure of the universe must admit only processes which cannot give rise to contradictions. We appeal to the process matrix formalism developed in the field of quantum foundations to characterise processes which are compatible with local free will whilst ruling out contradictions, and argue that this gives rise to ‘consistent chaining’ requirements that explain the temporal asymmetry of influence. We compare this view to the perspectival account of causation advocated by Price and Ramsey.
A Mathematical Framework For Operational Fine Tunings, Lorenzo Catani, Matthew Leifer
A Mathematical Framework For Operational Fine Tunings, Lorenzo Catani, Matthew Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings – already introduced by Wood and Spekkens in [NJP,17 …
High-Frequency Diode Effect In Superconducting Nb3Sn Microbridges, Sara Chahid, Serafim Teknowijoyo, Iris Mowgood, Armen Gulian
High-Frequency Diode Effect In Superconducting Nb3Sn Microbridges, Sara Chahid, Serafim Teknowijoyo, Iris Mowgood, Armen Gulian
Mathematics, Physics, and Computer Science Faculty Articles and Research
The superconducting diode effect has recently been reported in a variety of systems and different symmetry-breaking mechanisms have been examined. However, the frequency range of these potentially important devices still remains obscure. We investigated superconducting microbridges of Nb3Sn in out-of-plane magnetic fields; optimum magnetic fields of ∼10 mT generate ∼10% diode efficiency, while higher fields of ∼15–20 mT quench the effect. The diode changes its polarity with magnetic field reversal. We documented superconductive diode rectification at frequencies up to 100 kHz, the highest reported as of today. Interestingly, the bridge resistance during diode operation reaches a value that is a …
Golay Codes And Quantum Contextuality, Mordecai Waegell, P. K. Aravind
Golay Codes And Quantum Contextuality, Mordecai Waegell, P. K. Aravind
Mathematics, Physics, and Computer Science Faculty Articles and Research
It is shown that the codewords of the binary and ternary Golay codes can be converted into rays in RP23 and RP11 that provide proofs of the Kochen-Specker theorem in real state spaces of dimensions 24 and 12, respectively. Some implications of these results are discussed.
Does Science Need Intersubjectivity? The Problem Of Confirmation In Orthodox Interpretations Of Quantum Mechanics, Emily Adlam
Does Science Need Intersubjectivity? The Problem Of Confirmation In Orthodox Interpretations Of Quantum Mechanics, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of ‘orthodox interpretations,’ which includes QBism, neo-Copenhagen interpretations, and some versions of relational quantum mechanics. We demonstrate that intersubjectivity fails in radical ways in these approaches, and we explain why intersubjectivity matters for empirical confirmation. We take a detailed look at the way in which belief-updating might work in the kind of universe postulated by an orthodox interpretation, and argue that observers in such …
Black Holes, Disk Structures, And Cosmological Implications In E-Dimensional Space, Subhash Kak, Menas C. Kafatos
Black Holes, Disk Structures, And Cosmological Implications In E-Dimensional Space, Subhash Kak, Menas C. Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine a modern view of the universe that builds on achieved successes of quantum mechanics, general relativity, and information theory, bringing them together in integrated approach that is founded on the realization that space itself is e-dimensional. The global and local implications of noninteger dimensionality are examined, and how it may have increased from the value of zero to its current value is investigated. We find surprising aspects that tie to structures in the universe, black holes, and the role of observations.
What Is Nonclassical About Uncertainty Relations?, Lorenzo Catani, Matthew S. Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
What Is Nonclassical About Uncertainty Relations?, Lorenzo Catani, Matthew S. Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens
Mathematics, Physics, and Computer Science Faculty Articles and Research
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in …
Non-Inertial Quantum Clock Frames Lead To Non-Hermitian Dynamics, Ismael L. Paiva, Amit Te'eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov
Non-Inertial Quantum Clock Frames Lead To Non-Hermitian Dynamics, Ismael L. Paiva, Amit Te'eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle’s internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As …
Two Roads To Retrocausality, Emily Adlam
Two Roads To Retrocausality, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In recent years the quantum foundations community has seen increasing interest in the possibility of using retrocausality as a route to rejecting the conclusions of Bell’s theorem and restoring locality to quantum physics. On the other hand, it has also been argued that accepting nonlocality leads to a form of retrocausality. In this article we seek to elucidate the relationship between retrocausality and locality. We begin by providing a brief schema of the various ways in which violations of Bell’s inequalities might lead us to consider some form of retrocausality. We then consider some possible motivations for using retrocausality to …
Tabletop Experiments For Quantum Gravity Are Also Tests Of The Interpretation Of Quantum Mechanics, Emily Adlam
Tabletop Experiments For Quantum Gravity Are Also Tests Of The Interpretation Of Quantum Mechanics, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. In order to evaluate these experiments, we must determine if there is any interesting class of possibilities that will be convincingly ruled out if it turns out that gravity can indeed induce entanglement. In particular, since one argument for the significance of these experiments rests on the claim that they demonstrate the existence of superpositions of spacetimes, it is important to keep in mind that different interpretations of quantum mechanics may make different …
Watching The Clocks: Interpreting The Page-Wootters Formalism And The Internal Quantum Reference Frame Programme, Emily Adlam
Watching The Clocks: Interpreting The Page-Wootters Formalism And The Internal Quantum Reference Frame Programme, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous …
Weakness Of Weak Values: Incompatibility Of Anomalous Pulse-Spectrum Amplification And Optical Frequency Combs, John C. Howell
Weakness Of Weak Values: Incompatibility Of Anomalous Pulse-Spectrum Amplification And Optical Frequency Combs, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We probe the use of optical frequency combs to place lower bounds on anomalous amplification of a weak-value-measured pulse delay, potentially reaching a theoretical temporal resolution of better than 10−34 s. Owing to the interferometric behavior of weak values, we show that anomalous weak value amplification of a time delay is not equivalent to a temporal linear phase ramp. We show that the anomalous weak value is a rearrangement of amplitudes that generates an apparent shift that can be measured in direct detection, but does not change the actual frequency offset of a spectral distribution measurable in coherent detection. …
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.