Violations of Bell inequalities show that quantum entanglement produces nonclassical correlations between spatially separated systems. In quantum eraser experiments, interference is restored once distinguishability is removed. This highlights the essential role of distinguishability in quantum state transformations. However, it has not been recognized that a paradox can emerge using only conventional optical transformations of quantum states, and no experiment has been proposed to determine which of three mutually exclusive hypotheses outside the implicit assumptions of standard optical transformations and capable of resolving the paradox is realized in practice. Here we show that a paradox emerges in a configuration that reduces the distinguishability of an entangled state, and we propose an experiment capable of identifying which hypothesis is realized. Theory alone cannot determine which hypothesis is realized. Therefore, experimental verification is required. Regardless of the experimental outcome, the experiment would reveal an unrecognized property linking entanglement and distinguishability.
Violations of Bell inequalities show that quantum entanglement produces nonclassical correlations between spatially separated systems. In quantum eraser experiments, interference is restored once distinguishability is removed. This highlights the essential role of distinguishability in quantum state transformations. However, it has not been recognized that a paradox can emerge using only conventional optical transformations of quantum states, and no experiment has been proposed to determine which of three mutually exclusive hypotheses outside the implicit assumptions of standard optical transformations and capable of resolving the paradox is realized in practice. Here we show that a paradox emerges in a configuration that reduces the distinguishability of an entangled state, and we propose an experiment capable of identifying which hypothesis is realized. Theory alone cannot determine which hypothesis is realized. Therefore, experimental verification is required. Regardless of the experimental outcome, the experiment would reveal an unrecognized property linking entanglement and distinguishability.
Quantum entanglement is an essential principle in quantum mechanics, illustrating the relationship between two or more spatially separated particles.This correlation has been experimentally proven through various techniques, including the entangled photon experiment. Furthermore, the breach of Bell's inequality has confirmed that entanglement represents a genuine physical occurrence, which cannot be accounted for by local hidden variables, thus highlighting the peculiar characteristics of quantum mechanics. This article aims to introduce quantum entanglement and Bell's inequality, and to discuss the experiments conducted by Alain Aspect, John Clauser, and Anton Zeilinger, which paved the way for the development of quantum information science. Additionally, this paper will explore the potential applications of quantum technology in communication, cryptography, and computing, which rely on the exceptional properties of entanglement.
The EPR paradox was caused by the provision that quantum variables must have pre-existing values. This type of “hidden property realism” was later falsified by Bell’s Theorem. Yet, modern interpretations of quantum entanglement still insist on the reality of pre-existing properties, whether explicitly or implicitly. Instead, they treat Bell’s inequality as a Locality Criterion. This is a questionable practice, considering that classical joint measurements also violate such inequalities for mutually exclusive wave properties. In particular, consecutive measurements of polarization produce the same coefficients of correlation as parallel measurements with polarization-entangled quanta, yet they are explicitly local. Nonetheless, they also require nonlocal interpretations if pre-existing properties are taken for granted. The solution is to reject the models with pre-existing properties for both classical and quantum wave-like phenomena.
Violation of local realism via Bell inequality-a profound and counterintuitive manifestation of quantum theory that conflicts with the prediction of local realism-is viewed to be intimately linked with quantum entanglement. Experimental demonstrations of such a phenomenon using quantum entangled states are among the landmark experiments of modern physics and paved the way for quantum technology. Here, we report the violation of the Bell inequality that cannot be described by quantum entanglement in the system but arises from quantum indistinguishability by path identity, shown by the multiphoton frustrated interference. By analyzing the measurement of four-photon frustrated interference within the standard Bell-test formalism, we find a violation of Bell inequality by more than four SDs. Our work establishes a connection between quantum correlation and quantum indistinguishability, providing insights into the fundamental origin of the counterintuitive characteristics observed in quantum physics.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.
Entanglement and state distinguishability have long been central topics in quantum foundations. While each has developed into a rich subject in its own right, they can be connected through measurements in complementary bases. This connection provides insights into quantum and classical correlations and underlies many information-processing tasks, most notably quantum error correction (QEC). However, it has remained largely open whether the connection between entanglement and distinguishability extends to general measurements without assuming complementarity. We answer this question in the affirmative: the key is irreducibility induced by measurements, a much more relaxed condition than complementarity. Specifically, for POVMs satisfying an irreducibility condition, we establish a quantitative relation between the infidelity of one-sided local transformation into a maximally entangled state and the failure probability in state discrimination. We then characterize when both errors can vanish simultaneously. Our results have direct applications to entanglement distillation and QEC. Their errors can be certified by estimating classical input-output correlations from experimentally accessible local measurements, without requiring complementarity. The results also extend to quantum measurement theory. We derive novel trade-off relations that bridge two historically distinct approaches: information gain--irreversibility and observable noise--disturbance. Our connection between entanglement and distinguishability via irreducibility thus offers a common framework for entanglement distillation, QEC, and measurement trade-offs.