arXiv subjects

Jay Lawrence

Publications and source records attributed to Jay Lawrence.

17 recordsLinked to original sources

arXiv2026

Bell-EPR Correlations within Local Quantum Theory

We present a local unitary theory of a Bell-EPR measurement, starting with the premeasurement filtering of the individual photon polarizations and extending through the detection process involving four photodetectors, two at each receiving station. The essential feature is that decoherence occurs locally and independently with each detector upon its absorption of a photon. Communication between observers after they read their local outcomes confirms the known Bell-EPR correlations. This theory is manifestly local, but there exist other formulations, and interpretations, that are non-local.

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arXiv2025

The original Wigner's-Friend scenarios

We describe the Wigner's-Friend scenario according to Wigner, then a similar but earlier version according to Everett. Wigner and Everett provide different resolutions of essentially the same paradox. Decoherence theory provides a third resolution. Despite different interpretations (or their absence), these three stories fit together to form a consistent picture without a paradox.

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arXiv2023

Relational Quantum Mechanics is Still Incompatible with Quantum Mechanics

We showed in a recent article (Lawrence et. al., 2023, Quantum 7, 1015), that relative facts (outcomes), a central concept in Relational Quantum Mechanics, are inconsistent with Quantum Mechanics. We proved this by constructing a Wigner-Friend type sequential measurement scenario on a Greenberger-Horne-Zeilinger (GHZ) state of three qubits, and making the following assumption: "if an interpretation of quantum theory introduces some conceptualization of outcomes of a measurement, then probabilities of these outcomes must follow the quantum predictions as given by the Born rule." Our work has been criticized by Cavalcanti, Di Biagio, and Rovelli (CDR). In this note we show that their critique is invalid, and that their specific arguments raise questions of principle.

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arXiv2023

The Born Rule -- Axiom or Result?

The Born rule is part of the collapse axiom in the standard version of quantum theory, as presented by standard textbooks on the subject. We show here that its signature quadratic dependence follows from a single additional physical assumption beyond the other axioms - namely, that the probability of a particular measurement outcome (the state $\phi_k$, say) is independent of the choice of observable to be measured, so long as one of its eigenstates corresponds to that outcome. We call this assumption ``observable independence.'' As a consequence, the Born rule cannot be completely eliminated from the list of axioms, but it can, in principle, be reduced to a more physical statement. Our presentation is suitable for advanced undergraduates or graduate students who have taken a standard course in quantum theory. It does not depend on any particular interpretation of the theory.

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arXiv2022

Relative facts do not exist. Relational Quantum Mechanics is Incompatible with Quantum Mechanics. Response to the critique by Aur\'elien Drezet

In this comment we answer to the recent critique of our article [arXiv:2208.11793] about Relational Quantum Mechanics (RQM) by Aur\'elien Drezet [arXiv:2209.01237]. Here we point out that our critical analysis of RQM was precisely based on the most recent formulation of RQM, and that the theses found in the critique are based on neither RQM assumptions nor on our arguments.

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arXiv2022

Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory [see arXiv:2109.09170, which appears in the Oxford Handbook of the History of Interpretation of Quantum Physics]. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system $S$ and an observer $A$ without decoherence, and (ii) such an outcome is a "fact" relative to the observer $A$, but it is not a fact relative to another observer $B$ who has not interacted with $S$ or $A$ during the foregoing measurement process. For $B$ the system $S \otimes A$ remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.

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arXiv2022

Pointers for Quantum Measurement Theory

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a $d$-state particle we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the $d$ possible outcomes. We show that the unitary dynamics of the premeasurement process restricts the detector outputs to the subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states.

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arXiv2021

Observing a Quantum Measurement

With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of outcomes. This is done by inserting a quantum two-state system (an ancilla) in each path, capable of responding to the passage of the atom, and thus acting as a virtual detector. We then consider real measurements on the compound system of atomic spin and two ancillae. Nondestructive measurements of a set of compatible joint observables can be performed, one for a superposition and others for collapse properties. A novel perspective is given as to why, within unitary quantum theory, ordinary measurements are blind to such superpositions. Implications for the theory of measurement are discussed.

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arXiv2019

Many-qutrit Mermin inequalities with three measurement settings

Mermin inequalities are derived for systems of three-state particles (qutrits) employing three local measurement settings. These establish perfect correlations which violate local realistic bounds more strongly than those previously reported with two bases. The quantum eigenvalue of the Mermin operator grows as the dimension of the Hilbert space, $3^N$, rather than $2^N$, as obtained with two measurement bases. The number of distinct GHZ contradictions also increases as $3^N$.

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arXiv2017

Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium

We realize a $\Lambda$ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 8\,ms. We exponentially suppress the tunneling matrix elements involved in spontaneous energy relaxation by creating a "heavy" fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readout, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.

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arXiv2017

Mermin inequalities for perfect correlations in many-qutrit systems

The existence of GHZ contradictions in many-qutrit systems was a long-standing theoretical question until it's (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called M, in which every term has the chosen GHZ state as an eigenstate with eigenvalue unity. The quantum prediction for M is then just the number of concurrent observables, and this grows asymptotically as 2^N/3 as the number of qutrits (N) goes to infinity. The maximum classical value falls short for every N, so that the quantum to classical ratio (starting at 1.5 when N=3), diverges exponentially (~ 1.064^N) as N goes to infinity, where the system is in a Schroedinger cat-like superposition of three macroscopically distinct states.

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arXiv2015

Maximally Entangled States of Four Nonbinary Particles

Systems of four nonbinary particles, each having three or more internal states, exhibit maximally entangled states that are inaccessible to four qubits. This breaks the pattern of two- and three-particle systems, in which the existing graph states are equally accessible to binary and nonbinary systems alike. We compare the entanglement properties of these special states (called P-states) with those of the more familiar GHZ and cluster states accessible to qubits. The comparison includes familiar entanglement measures, the "steering" of states by projective measurements, and the probability that two such measurements, chosen at random, leave the remaining particles in a Bell state. These comparisons demonstrate not only that P-state entanglement is stronger than the other types, but that it is maximal in a well-defined sense. We prove that GHZ, cluster, and P-states represent all possible entanglement classes of four-particle graph states with a prime number (>2) of states per particle.

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arXiv2014

Rotational covariance and GHZ contradictions for three or more particles of any dimension

Greenberger-Horne-Zeilinger (GHZ) states are characterized by their transformation properties under a continuous symmetry group, and $N$-body operators that transform covariantly exhibit a wealth of GHZ contradictions. We show that local or noncontextual hidden variables cannot duplicate this covariance for any state-changing transformations, and we extract specific GHZ contradictions from discrete subgroups, with no restrictions on particle number $N$ or dimension $d$ except for the fundamental requirement that $N \geq 3$ for nonprobabilistic contradictions. However, the specific contradictions fall into three regimes distinguished by increasing demands on the number of measurement operators required for the proofs. We introduce new methods of proof that define these regimes. The first recovers theorems equivalent to those found recently by Ryu et. al. \cite{RLZL}, the first operator-based theorems for all odd dimensions, $d$, covering many (but not all) particle numbers $N$ for each $d$. The second and third produce new theorems that fill all remaining gaps down to $N=3$, for every $d$. The common origin of all such GHZ contradictions is that the GHZ states and measurement operators transform according to different representations of the symmetry group, which has an intuitive physical interpretation.

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arXiv2011

Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles

A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in p+1 bases (not necessarily the same ones), and totally entangled in the remaining p^N-p. It follows that the maximum number of product bases is p+1, and when this number is realized, all remaining p^N-p bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for two qupits (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits and qutrits. With three qupits there are three MUB types, and a number of combinations (p+2) are possible in full complements. With N=4, there are 6 MUB types for p=2, but new MUB types become possible with larger p, and these are essential to the realization of full complements. With this example, we argue that new MUB types, showing new entanglement characteristics, should enter with every step in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs should play critical roles in filling complements.

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arXiv2005

Rotational Properties and GHZ Contradictions in N-Qubit Systems

Rotational symmetries of N-qubit Greenberger-Horne-Zeilinger (GHZ) states directly exhibit their nonlocality and render transparent the many possible measurements that produce absolute contradictions with local realism. While N measurements fix the assumed elements of reality, an exponentially growing number of absolute contradictions occurs. Operators that represent the detector settings provide a faithful representation of the symmetry group, and demonstrate Kochen-Specker contextuality.

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arXiv2004

Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure allowing for the coexistence of separable, partially-entangled, and totally entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.

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arXiv2002

Mutually unbiased binary observable sets on N qubits

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each consisting of 2^N-1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.

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