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Articles 151 - 180 of 252
Full-Text Articles in Quantum Physics
Weak Values Are Quantum: You Can Bet On It, Alessandro Romito, Andrew N. Jordan, Yakir Aharonov, Yuval Gefen
Weak Values Are Quantum: You Can Bet On It, Alessandro Romito, Andrew N. Jordan, Yakir Aharonov, Yuval Gefen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The outcome of a weak quantum measurement conditioned to a subsequent post-selection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective measurements. However, a classical model has been recently put forward that can reproduce peculiar expectation values, reminiscent of weak values. This led the authors of that work to claim that weak values have an entirely classical explanation. Here we discuss what is quantum about weak values with the help of a simple model based on basic quantum mechanics. We first demonstrate how a classical theory can indeed …
Quantum Violation Of The Pigeonhole Principle And The Nature Of Quantum Correlations, Yakir Aharonov, Fabrizio Colombo, S. Popescu, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen
Quantum Violation Of The Pigeonhole Principle And The Nature Of Quantum Correlations, Yakir Aharonov, Fabrizio Colombo, S. Popescu, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum …
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Retrocausal models of quantum mechanics add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Physical law therefore enables prophecy of future events only as long as this prophecy is not revealed to a free agent who can otherwise render it …
Review Of Douglas Stone, Einstein And The Quantum: The Quest Of The Valiant Swabian, Matthew S. Leifer
Review Of Douglas Stone, Einstein And The Quantum: The Quest Of The Valiant Swabian, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A book review of A. Douglas Stone's Einstein and the Quantum: The Quest of the Valiant Swabian.
Interference Energy Spectrum Of The Infinite Square Well, Mordecai Waegell, Yakir Aharonov, Taylor Lee Patti
Interference Energy Spectrum Of The Infinite Square Well, Mordecai Waegell, Yakir Aharonov, Taylor Lee Patti
Mathematics, Physics, and Computer Science Faculty Articles and Research
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of …
No Return To Classical Reality, David Jennings, Matthew S. Leifer
No Return To Classical Reality, David Jennings, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by rst granting quite …
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and …
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator. Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates are better discriminated by measurement than the bare states. Furthermore, we show that when the resonator leaks much …
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Are the electromagnetic scalar and vector potentials dispensable? Vaidman [Phys. Rev. A 86, 040101(R) (2012)] has suggested that local interactions of gauge-invariant quantities, e.g., magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities, and, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Mathematics, Physics, and Computer Science Faculty Articles and Research
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger’s famous remark about it [Proc. Cambridge Philos. Soc. 31, 555 (1935)], prompts the examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments and report here values of the Bell parameter greater than ℬ=2.54. This is many standard deviations outside the limit ℬ=2 established by the Clauser–Horne–Shimony–Holt Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson …
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Current methods for measuring magnetic flux are based on performing many measurements over a large ensemble of electrons. We propose a novel method based on wave function "revival" for measuring the flux modulo using only a single electron. A preliminary analysis of the feasibility of the experiment is provided.
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a nonguess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and nonguess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case.We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement.Notably, while the cost advantage …
Can A Future Choice Affect A Past Measurement's Outcome?, Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur
Can A Future Choice Affect A Past Measurement's Outcome?, Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur
Mathematics, Physics, and Computer Science Faculty Articles and Research
An EPR experiment is studied where each particle within the entangled pair undergoes a few weak measurements (WMs) along some pre-set spin orientations, with the outcomes individually recorded. Then the particle undergoes one strong measurement along an orientation chosen at the last moment. Bell-inequality violation is expected between the two final measurements within each EPR pair. At the same time, statistical agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction seemingly ensues: (i) Bell’s theorem forbids spin values to exist prior to the choice of the orientation measured; (ii) A weak …
Weak Values As Interference Phenomena, Justin Dressel
Weak Values As Interference Phenomena, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement. These averages can exceed the eigenvalue range of the observable ostensibly being estimated, which has prompted considerable debate regarding their interpretation. Classical conditioned averages of noisy signals only show such anomalies if the quantity being measured is also disturbed prior to conditioning. This fact has recently been rediscovered, along with the question whether anomalous weak values are merely classical disturbance effects. Here we carefully review …
Heisenberg Scaling With Weak Measurement: A Quantum State Discrimination Point Of View, Andrew N. Jordan, Jeff Tollaksen, James E. Troupe, Justin Dressel, Yakir Aharonov
Heisenberg Scaling With Weak Measurement: A Quantum State Discrimination Point Of View, Andrew N. Jordan, Jeff Tollaksen, James E. Troupe, Justin Dressel, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the results of the paper “Precision metrology using weak measurements” (Zhang et al. arXiv:1310.5302, 2013) from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the precision of the interaction parameter between coherent light and a spin one-half particle (or pseudo-spin) has a simple interpretation in terms of the interaction rotating the quantum state to an orthogonal one. To achieve this scaling, the information must be extracted from the spin rather than from the coherent state of light, limiting the applications of the method to phenomena such as cross-phase modulation. …
Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen
Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen
Philosophy Faculty Articles and Research
The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak values, introduced more than 25 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource in photonics for exploring foundations of quantum mechanics, as well as a practical laboratory tool. Due to the tiny coherence volume of particles used in matter-wave optics, a straightforward implementation of weak measurements is not feasible. We have overcome this hurdle by developing a method to weakly measure a massive particle's spin component. A neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom. Here, we present how one …
Fundamental Mathematics Of Consciousness, Menas Kafatos
Fundamental Mathematics Of Consciousness, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.
Logical Pre- And Post-Selection Paradoxes Are Proofs Of Contextuality, Matthew F. Pusey, Matthew S. Leifer
Logical Pre- And Post-Selection Paradoxes Are Proofs Of Contextuality, Matthew F. Pusey, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
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 Lüders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [Phys. Rev. Lett. 95, 200405] identified a striking class of such paradoxes, known as logical pre- and postselection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version …
Conservation Of The Spin And Orbital Angular Momenta In Electromagnetism, Konstantin Y. Bliokh, Justin Dressel, Franco Nori
Conservation Of The Spin And Orbital Angular Momenta In Electromagnetism, Konstantin Y. Bliokh, Justin Dressel, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We review and re-examine the description and separation of the spin and orbital angular momenta (AM) of an electromagnetic field in free space. While the spin and orbital AM of light are not separately meaningful physical quantities in orthodox quantum mechanics or classical field theory, these quantities are routinely measured and used for applications in optics. A meaningful quantum description of the spin and orbital AM of light was recently provided by several authors, which describes separately conserved and measurable integral values of these quantities. However, the electromagnetic field theory still lacks corresponding locally conserved spin and orbital AM currents. …
Implementing Generalized Measurements With Superconducting Qubits, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Implementing Generalized Measurements With Superconducting Qubits, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. First, we consider two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup and using an indirect ancilla qubit measurement. Second, we decompose an arbitrary purity-preserving two-outcome measurement into single-qubit unitary rotations and a partial projection. Third, we systematically reduce any multiple-outcome measurement to a sequence of such two-outcome measurements and unitary operations. Finally, we consider how to define suitable fidelity measures for multiple-outcome generalized measurements.
Mapping The Optimal Route Between Two Quantum States, S. J. Weber, A. Chantasri, Justin Dressel, Andrew N. Jordan, K. W. Murch, I. Siddiqi
Mapping The Optimal Route Between Two Quantum States, S. J. Weber, A. Chantasri, Justin Dressel, Andrew N. Jordan, K. W. Murch, I. Siddiqi
Mathematics, Physics, and Computer Science Faculty Articles and Research
A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance1 to chemical synthesis2. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories3, 4, 5 of a superconducting circuit that evolves under the …
Entanglement-Assisted Weak Value Amplification, Shengshi Pang, Justin Dressel, Todd A. Brun
Entanglement-Assisted Weak Value Amplification, Shengshi Pang, Justin Dressel, Todd A. Brun
Mathematics, Physics, and Computer Science Faculty Articles and Research
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting n ancillas, the postselection probability can be increased by a factor of n while keeping the weak value fixed (compared to n …
The Problem Of Confirmation In The Everett Interpretation, Emily Adlam
The Problem Of Confirmation In The Everett Interpretation, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to form true beliefs. I show that in an Everettian context, the experimental evidence that we have available could not provide empirical confirmation for quantum mechanics, and moreover that we would not even be able to establish reference to the theoretical entities of quantum mechanics. I then consider a range of existing Everettian approaches to the probability problem and show that they …
Colloquium: Understanding Quantum Weak Values: Basics And Applications, Justin Dressel, Mehul Malik, Filippo M. Miatto, Andrew N. Jordan, Robert W. Boyd
Colloquium: Understanding Quantum Weak Values: Basics And Applications, Justin Dressel, Mehul Malik, Filippo M. Miatto, Andrew N. Jordan, Robert W. Boyd
Mathematics, Physics, and Computer Science Faculty Articles and Research
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a …
Classical Field Approach To Quantum Weak Measurements, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Classical Field Approach To Quantum Weak Measurements, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be …
Certainty In Heisenberg’S Uncertainty Principle: Revisiting Definitions For Estimation Errors And Disturbance, Justin Dressel, Franco Nori
Certainty In Heisenberg’S Uncertainty Principle: Revisiting Definitions For Estimation Errors And Disturbance, Justin Dressel, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as meansquared deviations relies on an implicit assumption that is generally incompatible with the Bell-Kochen-Specker- Spekkens contextuality theorems, and which results in averaging the deviations over a non-positive-semidefinite joint quasiprobability distribution. For unbiased measurements, the error admits a concrete interpretation as the dispersion in the estimation of the mean induced by the measurement ambiguity.We demonstrate how to directly measure not only this dispersion but also every observable moment with …
Avoiding Loopholes With Hybrid Bell-Leggett-Garg Inequalities, Justin Dressel, Alexander N. Korotkov
Avoiding Loopholes With Hybrid Bell-Leggett-Garg Inequalities, Justin Dressel, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
By combining the postulates of macrorealism with Bell locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally invasive measurements can be used, which avoids the “clumsiness” Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the “disjoint sampling” Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell locality or a preparation conspiracy …