It is shown that a standard one-dimensional coined discrete-time quantum walk can generate operationally admissible post-quantum correlations in a coin-position Bell scenario, without any modification of its unitary nearest-neighbor dynamics. Post-quantum features enter exclusively through an extended operational preparation of the coin, described by a complementarity-violating Hermitian trace-one operator, while physical consistency is enforced solely at the level of observable statistics via admissibility and no-signaling. The extended preparation admits an experimental emulation through a two-component quasiprobability reconstruction over physical coin states, at the price of an increased sampling overhead. The walk-generated coin-position entanglement can support CHSH values exceeding Tsirelson's bound, even though the walk dynamics remains fully standard. We also show that physically natural coarse-grained position measurements can render such post-quantum correlations operationally inaccessible, strongly suppressing observable Bell violations. The purpose here is to contrast the separation between the existence of post-quantum behavior and its accessibility under realistic measurement constraints.
It is shown that a standard one-dimensional coined discrete-time quantum walk can generate operationally admissible post-quantum correlations in a coin-position Bell scenario, without any modification of its unitary nearest-neighbor dynamics. Post-quantum features enter exclusively through an extended operational preparation of the coin, described by a complementarity-violating Hermitian trace-one operator, while physical consistency is enforced solely at the level of observable statistics via admissibility and no-signaling. The extended preparation admits an experimental emulation through a two-component quasiprobability reconstruction over physical coin states, at the price of an increased sampling overhead. The walk-generated coin-position entanglement can support CHSH values exceeding Tsirelson's bound, even though the walk dynamics remains fully standard. We also show that physically natural coarse-grained position measurements can render such post-quantum correlations operationally inaccessible, strongly suppressing observable Bell violations. The purpose here is to contrast the separation between the existence of post-quantum behavior and its accessibility under realistic measurement constraints.
Violations of Bell inequalities are a hallmark of entanglement, with only entangled states capable of exceeding classical bounds in standard Bell tests. Here we analyze anomalous weak values of the CHSH-Bell operator in pre- and post-selected (PPS) quantum ensembles, using them to define separability-constrained bounds on Bell-type nonlocal correlations in the presence of post-selection. Fixing the overlap between the pre- and post-selected states, we compare three scenarios: unrestricted boundary states, one separable boundary state, and both boundary states separable. For each case, we derive both the maximal weak value for a fixed Bell operator and the maximal bound obtained by further optimizing over all CHSH operators. Our results show that post-selection and entanglement are distinct operational resources: post-selection alone can enhance correlations, but entanglement is necessary to exceed the corresponding separable PPS bounds, and their combination yields the strongest attainable correlations. Thus the separable PPS bound plays the role of a post-selected separability benchmark, distinct from the standard Bell bound. We further show that the enhancement beyond the separable bound closely tracks the concurrence of the states that optimize the bounds, identifying entanglement as the source of the additional correlation strength. Finally, we show that nonlocal weak values provide post-selected entanglement witnesses, and we give a constructive protocol that detects every pure two-qubit source state with nonzero concurrence in the ideal state-adapted setting, even in regimes where the corresponding standard CHSH entanglement test is inconclusive. More broadly, our results motivate hybrid protocols that combine post-selection and entanglement, with possible applications to improved quantum sensing, weak-value amplification, and quantum information processing.
Discrete-time quantum walks provide a versatile framework for investigating the generation, redistribution, and transport of quantum correlations in composite quantum systems. Here, we study the dynamics of bipartite and genuine multipartite entanglement in a two-walker discrete-time quantum walk on a one-dimensional lattice. By employing logarithmic negativity and the generalized geometric measure (GGM), we systematically characterize the redistribution of bipartite entanglement among different subsystem partitions and the emergence of genuine multipartite entanglement involving the two coin and two position degrees of freedom. We show that the entanglement dynamics are strongly influenced by the lattice topology. The open-boundary regime exhibits a monotonic redistribution of quantum correlations, whereas the closed-boundary regime gives rise to pronounced oscillatory behavior due to boundary-induced interference and recurrent wave-packet overlap. In the open-boundary regime, the GGM rapidly approaches its theoretical maximum value of 1/2 and remains largely insensitive to the choice of the initial Bell state as well as to continuous variations of the local coin operator over a broad parameter range, except near the Pauli-X coin. These results demonstrate that maximal genuine multipartite entanglement generation is a robust and generic feature of open-boundary two-walker discrete-time quantum walks, establishing them as promising platforms for engineering multipartite quantum correlations in quantum information processing and quantum simulation.
Randomness is the essence of many processes in nature and human society. It can provide important insights into phenomena as diverse as disease transmission, financial markets, and signal processing. Quantum randomness is intrinsically different from classical stochasticity since it is affected by interference and entanglement. Quantum walks profit from the entanglement that is built up between a walker's position and the "coin" degree of freedom that determines the direction of a walker's motion. This entanglement makes quantum walks promising candidates for the implementation of quantum computational algorithms and as a detector of quantum behavior. While several proof-of-principle quantum walk experiments have recently been implemented, the walk scheme we demonstrate here involves the synthesis of the atom-optics kicked rotor with the dynamics of a state selective ratchet realized with a Bose-Einstein condensate. Here we present a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. To implement each step of the walk, i.e. a coin toss followed by a unitary shift operator, we use a microwave pulse, which produces a superposition of two internal states, and a resonant quantum ratchet, which entangles the internal and external degrees of freedom. Our quantum ratchet, whose direction at each step depends on the result of the coin toss, is realized by the atom-optics kicked rotor. We demonstrate the principle features of a standard quantum walk, contrasting them to the behavior of a classical walk. In addition, by manipulating either the walk or coin operator we show how the walk dynamics can be biased or reversed. Furthermore, we show the quantum-to-classical transition in our walk, via randomizing the mixing between the two internal states during each coin toss. Our walk offers distinct advantages arising from the robustness of its dynamics in momentum space, extendability to higher dimensions, and possible dependence on many-body correlations.
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions (δ, δ′, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine the maximal entanglement that can be rigorously generated for any step beyond the second regardless of initial conditions with appropriate coin sequences. The simplest coin sequence comprising Hadamard and identity operations is equivalent to the generalized elephant quantum walk, which exhibits an increasingly faster spreading in terms of probability distribution. Experimentally, we demonstrate a ten-step quantum walk driven by such coin sequences with linear optics and thereby show the desired high-dimensional bipartite entanglement as well as the transport behavior of faster spreading.
This work investigates a discrete-time quantum walk on a one-dimensional lattice driven by three entangled coins, each initialized via a Hadamard operator. The walker moves only when all three coins yield identical outcomes (HHH or TTT), coupling an 8-dimensional coin Hilbert space to the position degree of freedom. We analyze fully separable, fully entangled, and intermediate initial coin states, computing the von Neumann entropy of reduced subsystems to derive the mutual information between coin and position over successive steps. Our results demonstrate that initial tripartite entanglement significantly accelerates the growth of mutual information and enhances coin-position correlations compared to separable initial conditions. Notably, GHZ-type entangled states exhibit non-monotonic short-time dynamics due to interference, yet ultimately yield up to 18% higher mutual information by the tenth step. These findings underscore the role of pre-walk entanglement as a resource for controlling information flow and spatial spreading in quantum-walk-based protocols, with implications for quantum transport, state transfer, and correlation engineering.