We investigate the experimental prospects for testing a relativistic local quantum measurement inequality that quantifies the trade-off between vacuum insensitivity and responsiveness to excitations for finite-size detectors. Building on the Reeh--Schlieder approximation for coherent states, we derive an explicit and practically applicable bound for arbitrary coherent states. To connect with realistic photodetection scenarios, we model the detection region as a square prism operating over a finite time window and consider a normally incident single-mode coherent state. Numerical results exhibit the expected qualitative behavior: suppressing dark counts necessarily tightens the achievable click probability.
We investigate the experimental prospects for testing a relativistic local quantum measurement inequality that quantifies the trade-off between vacuum insensitivity and responsiveness to excitations for finite-size detectors. Building on the Reeh--Schlieder approximation for coherent states, we derive an explicit and practically applicable bound for arbitrary coherent states. To connect with realistic photodetection scenarios, we model the detection region as a square prism operating over a finite time window and consider a normally incident single-mode coherent state. Numerical results exhibit the expected qualitative behavior: suppressing dark counts necessarily tightens the achievable click probability.
We investigate the trade-off between vacuum insensitivity and sensitivity to excitations in finite-size detectors, taking measurement locality as a fundamental constraint. We derive an upper bound on the detectability of vacuum excitation, given a small but nonzero probability of false positives in the vacuum state. The result is independent of the specific details of the measurement or the underlying physical mechanisms of the detector and relies only on the assumption of locality. Experimental confirmation or violation of the inequality would provide a test of the axioms of algebraic quantum field theory, offer new insights into the measurement problem in relativistic quantum physics, and establish a fundamental technological limit in local particle detection.
We review what it means for a relativistic particle to be localized and argue that the most useful approach is through local measurement. This perspective ties localization directly to relativistic causality and measurable outcomes in spacetime. Strict localization in quantum field theory is formalized by states that give the same expectation value as vacuum for all local observables outside some spacetime region. With this formalism, single photons cannot be strictly localized, but coherent states can. The structure and interpretation of local observables and local operator algebras are discussed in connection with the Reeh-Schlieder theorem. Since probabilities of local measurement outcomes cannot vanish in vacuum, particle detection events must be phrased carefully. Key characteristics of strictly localized states are surveyed alongside concrete strategies for constructing them. The relationship between localization, causality, and on-demand sources is analyzed, finding that strictly localized states can represent localized, propagating information in quantum field theory. Explicit examples of localized photonic states are presented with an emphasis on quantum optics, including states that approximate single photons and (entangled) Bell states.
In this work, we deal with the relaxation of two central assumptions in standard locally realistic hidden variable (LRHV) inequalities: free will in choosing measurement settings, and the presence of perfect detectors at the measurement devices. Quantum correlations violating LRHV inequalities are called quantum nonlocal correlations. In principle, in an adversarial situation, there could be a hidden variable introducing bias in the selection of measurement settings, but observers with no access to that hidden variable could be unaware of the bias. In practice, however, detectors do not have perfect efficiency. A main focus of this paper is the introduction of the framework in which given a quantum state with nonlocal behavior under constrained free will, we can determine the threshold values of detector parameters (detector inefficiency and dark counts) such that the detectors are robust enough to certify nonlocality. We also introduce a class of LRHV inequalities with constrained free will, and we discuss their implications in the testing of quantum nonlocal correlations.
Cross-click operators, the POVM elements for simultaneous clicks in detectors assigned to different measurement bases, are used in QKD and entanglement-verification analyses with realistic threshold detectors to bound multiphoton contributions. Earlier applications verified the needed growth of the minimum eigenvalue f(n) on the n-photon subspace only numerically over finite sectors. This work gives an analytic characterization for passive linear-optical analyzers with arbitrary efficiency mismatch and dark counts. The key observation is that every silence operator is the second quantization Γ(A) of an explicit single-photon contraction A, whose n-photon restriction is A⊗n on Symn. This yields: (i) monotonicity f(n+1)≥f(n); (ii) two-sided exponential bounds maxbγb∣Ab∣n≤1−f(n)≤∑bγb∣Ab∣n, which determine the exact asymptotic convergence rate from single-photon spectral data; (iii) for ideal detectors and n≥1, the exact formula f(n)=1−∑bpbn; and (iv) an exact factorization 1−f(nA,nB)=(1−fA(nA))(1−fB(nB)) for the two-party cross-click operator. The results apply to polarization, time-bin, and spatial-mode analyzers within the stated threshold-detector model. As an application, we obtain closed-form photon-number weight bounds used in detection-efficiency-mismatch analyses, replacing finite-sector Fock-space numerics by formulas valid for all photon numbers.
Reliable and loophole-free demonstrations of the violation of local realism (LR) are highly desirable not only for understanding the foundation of quantum mechanics but also for facilitating quantum information processing, such as quantum key distribution and randomness expansion. To date, LR has been experimentally violated, but with loopholes, by testing predetermined Bell inequalities. This thesis presents a framework for verifying and quantifying the violation of LR without relying on a particular Bell inequality.\nFirst, the experimental resources, such as the quantum state, measurement settings, detection effciency, and visibility required for a violation of LR, are studied via a measure called the statistical strength. The higher the statistical strength, the more confidence in a violation of LR one has after a suffciently large number of experimental data. Particularly, we study the minimum detection effciency required to achieve any given statistical strength level in tests of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. It is shown that, compared with photon detectors, photon counters make violations of LR easier to detect for any nonzero probability of multiple photons in an output beam of the polarizing beam splitter.\nSecond, to quantify the statistical evidence against LR obtained from a finite number of experimental data, one can choose a test statistic, such as a Bell-inequality violation, to measure the amount of violation of LR. It is desirable to bound the probability, according to LR, of obtaining a test statistic at least as extreme as that observed. This probability is known as a p-value for the hypothesis test of LR. We propose a protocol to bound such a p-value. The bound provided is asymptotically tight, if the prepared quantum state and measurement settings are stable during an experiment. Therefore, the proposed protocol is asymptotically optimal, and the bound provided is a standardized measure of success for experimental tests of LR. One can quantitatively compare different experimental tests based on this bound. Moreover, the bound provided is valid even if the quantum state varies arbitrarily and local realistic models depend on previous measurement settings and outcomes. Hence, this bound facilitates device-independent and nonlocality-based quantum information processing. For comparison, bounds of p-values derived from Bell-inequality violations using the number of standard deviations of violation of a Bell inequality or using martingale theory are studied. It is found that putative bounds derived from the number of standard deviations of violation are not valid and bounds from martingale theory are not tight.\nFinally, a simplified and effcient data analysis protocol using a set of Bell inequalities is proposed and compared with the above optimal and martingale-based protocols. The simplified protocol provides as good as and typically tighter p-value bounds than the martingale-based protocol, and the bounds provided can even be asymptotically tight. Moreover, the simplified protocol can be applied to any test with linear witnesses, such as tests for verifying entanglement, system dimensionality, or steering.