Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breaking such a property does not hold in general, though for certain channels and for a restricted class of states for all channels this holds.We also consider channels whose output remains local under SLOCC and call them `strongly non-locality breaking'.
We provide a closed form necessary-sufficient condition for any two-qubit state to show hidden CHSH nonlocality, which is likely to be useful for other purposes as well. This in turn allows us to characterize all strongly non-locality breaking qubit channels. It turns out that unital qubit channels breaking nonlocality of maximally entangled states are strongly non-locality breaking while extremal qubit channels cannot be so unless they are entanglement breaking.
Non-locality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Different from 2-qubit case, it is shown that non-locality sharing between $\mathrm{Alice_{1}-Bob_{1}-Charlie_{1}}$ and $\mathrm{Alice_{2}-Bob_{2}-Charlie_{2}}$ in 3-qubit system can be observed, where two Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities can be violated simultaneously. What's more, a complete non-locality sharing with 8 MABK inequalities violations simultaneously can be also observed. Compared with 2-qubit case, the nonlocal sharing in a three qubit system shows mo…
Due to the short decohorence time of qubits available in the NISQ-era, it is essential to pack (minimize the size and or the depth of) a logical quantum circuit as efficiently as possible given a sparsely coupled physical architecture. In this work we introduce a locality-aware qubit routing algorithm based on a graph theoretic framework. Our algorithm is designed for the grid and certain "grid-like" architectures. We experimentally show the competitiveness of algorithm by comparing it against the approximate token swapping algorithm, which is used as a primitive in many state-of-the-art quant…
Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical …
It is shown that having degenerate ground states over the domain of the wavefunction of a system is a sufficient condition for a quantum system to act as a measuring apparatus for the system. Measurements are then instances of spontaneous symmetry breaking to one of these ground states, induced by environmental perturbations. Together with non-Boolean holism this constitutes an optimal formulation of quantum mechanics that does not imply non-locality.
We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non-LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreas…
Non-classical probability is the underlying feature of quantum mechanics. The emergence of Bell-CHSH non-locality for bipartite systems and linear entanglement inequalities for two-qubit systems has been shown in Adhikary et al. 2020 [Eur. Phys. J. D 74, 68 (2020)], purely as violations of classical probability rules. In this paper, we improve upon that work by showing that violation of any nonlocality inequality implies violation of classical probability rules, manifested through negative probabilities, without recourse to any underlying theory. Moving on to entanglement, we employ parent pse…
Non-Markovian evolutions are responsible for a wide variety of physically interesting effects. Here, we study non-locality of the non-classical state of a system consisting of a qubit and an oscillator exposed to the effects of non-Markovian evolutions. We find that the different facets of non-Markovianity affect non-locality in different and non-obvious ways: ranging from pronounced insensitivity of the Bell function to quite a spectacular evidence of information kick-back.
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
The non-local properties of the noisy three-qubit Greenberger-Horne-Zeilinger (GHZ) states parameterized by the visibility 0<v<1 are investigated. Based on the violation of the 2x2x2-setting Mermin inequality, the noisy three-qubit GHZ states are non-local for the parameter range 1/2<v<1. It has been posed whether additional settings would allow to lower the threshold visibility. Here we report on Bell inequalities giving a threshold value smaller than v=1/2. This rules out the possibility of a local hidden variable model in the limit of v=1/2. In particular, the lowest threshold visibility we…
Hardy's paradox (equivalently, Hardy's non-locality or Hardy's test) [\href{https://link.aps.org/doi/10.1103/PhysRevLett.68.2981}{L. Hardy, Phys. Rev. Lett. \textbf{68}, 2981 (1992)}] is used to show non-locality without inequalities and it has been tested several times using optical circuits. We, for the first time, experimentally test Hardy's paradox of non-locality in superconducting qubits. For practical verification of Hardy's paradox, we argue that the error-modeling used in optical circuits is not useful for superconducting qubits. So, we propose a new error-modeling for Hardy's paradox…
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides threequbit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have…
Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of t…
We study entanglement and non-locality of connected four-qubit hypergraph states. One obtains the SLOCC classification from the known LU-orbits. We then consider Mermin's polynomials and show that all four-qubit hypergraph states exhibit non-local behavior. Finally, we implement some of the corresponding inequalities on the IBM Quantum Experience.
The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work, we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin \emph{et. al.} in https://doi.org/10.1103/PhysRevA.9…
Bell's theorem states that, to simulate the correlations created by measurement on pure entangled quantum states, shared randomness is not enough: some "non-local" resources are required. It has been demonstrated recently that all projective measurements on the maximally entangled state of two qubits can be simulated with a single use of a "non-local machine". We prove that a strictly larger amount of this non-local resource is required for the simulation of pure non-maximally entangled states of two qubits $\ket{ψ(α)}= \cosα\ket{00}+\sinα\ket{11}$ with $0<α\lesssim\fracπ{7.8}$.
The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of {\it classicality} as the non-violation of these classical inequalities by quantum states of several multiqubit systems and compare it with the non-violation of Bell inequalities, that is, {\it locality}. We explore --numerically and analytically-- the relationship between several other quantum measures and discover the deep connection existing between them. The results are surprising due to the fact that these measures are very differ…
We prove that for a three-qubit system in the Greenberger-Horne-Zeilinger (GHZ) state, locality per se is in conflict with the perfect GHZ correlations. The proof does not in any way use the realism assumption and can lead to a refutation of locality. We also provide inequalities that are imposed by locality. The experimental confirmation of the present reasoning may imply a genuine quantum nonlocality and will deepen our understanding of nonlocality of nature.
We provide a detailed description of the EPR paradox (in the Bohm version) for a two qubit-state in the discrete Wigner function formalism. We compare the probability distributions for two qubit relevant to simultaneously-measurable observables (computed from the Wigner function) with the probability distributions representing two perfectly-correlated classic particles in a discrete phase-space. We write in both cases the updating formulae after a measure, thus obtaining a mathematical definition of \textit{classic collapse} and \textit{quantum collapse}. We study, with the EPR experiment, the…
It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally -- notwithstanding Bell's theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit's local description is shown to grow exponentially with the total number of qubits considered as a gl…
Fermion-to-qubit mappings that preserve geometric locality are especially useful for simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. They avoid the overhead associated with geometric non-local parity terms in mappings such as the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. As a result, they often provide quantum circuits with lower depth and gate complexity. In such encodings, fermionic states are encoded in the common +1 eigenspace of a set of stabilizers, akin to stabilizer quantum error-correcting codes. Here, we discuss several know…
The present paper is both a review on the Feynman problem, and an original research presentation on the relations between Fermionic theories and qubits theories, both regarded in the novel framework of operational probabilistic theories. The most relevant results about the Feynman problem of simulating Fermions with qubits are reviewed, and in the light of the new original results the problem is solved. The answer is twofold. On the computational side the two theories are equivalent, as shown by Bravyi and Kitaev (Ann. Phys. 298.1 (2002): 210-226). On the operational side the quantum theory of…
The unique entanglement measure is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the non-locality. For justification, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only considering one entanglement measure, the numerical result contradicts expectation. Therefore, we conclude ``Non-Locality$\neq$Quantum Entanglement''. We propose the generalized $R$-matrix or correlation matrix f…
The insight due to John Bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day. We describe an experiment, and its analysis, displaying non-locality of entangled qutrit pairs. The non-locality of such systems, as compared to qubit pairs, is of particular interest since it potentially opens the door for tests of bipartite non-local behavior independent of probabilistic Bell inequalities, but of deterministic nature.
Cluster states are multi-particle entangled states with special entanglement properties particularly suitable for quantum computation. It has been shown that cluster states can exhibit Greenberger-Horne-Zeilinger (GHZ)-type non-locality even when some of their qubits have been lost. In the present work, we generated a four-photon mixed state, which is equivalent to the partial, qubit-loss state of an N-qubit cluster state up to some local transformations. By using this mixed state, we then realize a GHZ-type violation of local realism. Our results not only demonstrate a mixed state's GHZ-type …
Incompatibility and nonlocality are not only of foundational interest but also act as important resources for quantum information theory. In the Clauser-Horne-Shimony-Holt (CHSH) scenario, the incompatibility of a pair of observables is known to be equivalent to Bell nonlocality. Here, we investigate these notions in the context of qubit channels. The Bell-CHSH inequality has a greater perspective--compared to any genuine tripartite nonlocality scenario--while determining the interplay between nonlocality breaking qubit channels and incompatibility breaking qubit channels. In the Bell-CHSH sce…
The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $ϕ^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution…
In this note, we discuss a closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality. This is then used to numerically compute the relative volume of states showing hidden Bell-CHSH non-locality , among all two-qubit states with one-sided reduction maximally mixed.
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used t…
We investigate theoretically the model of two \qubits" system (one qubit having an auxiliary level) interacting with a single-mode resonator in the ultrastrong coupling regime. We show that a single photon could simultaneously excite two qubits without breaking the parity symmetry of system by properly encoding the excited states of qubits. The optimal parameter regime for achieving high probability approaching one is identified in the case of ignoring the system dissipation. Moreover, using experimentally feasible parameters, we also analyze the dissipation dynamics of the system, and present…
We investigate both theoretically and experimentally the dynamics of entanglement and non-locality for two qubits immersed in a global pure dephasing environment. We demonstrate the existence of a class of states for which entanglement is forever frozen during the dynamics, even if the state of the system does evolve. At the same time non-local correlations, quantified by the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, either undergo sudden death or are trapped during the dynamics.
Multipartite nonlocality in a network is conceptually different from standard multipartite Bell nonlocality. In recent times, network nonlocality has been studied for various topologies. We consider a linear-chain topology of the network and demonstrate the quantum nonlocality (the non-$n$-locality). Such a network scenario involves $n$ number of independent sources and $n+1$ parties, two edge parties (Alice and Charlie), and $n-1$ central parties (Bobs). It is commonly assumed that each party receives only two inputs. In this work, we consider a generalized scenario where the edge parties rec…
The (non-)local content in the sense of Elitzur, Popescu, and Rohrlich (EPR2) [Phys. Lett. A 162, 25 (1992)] is a natural measure for the (non-)locality of quantum states. Its computation is in general difficult, even in low dimensions, and is one of the few open questions about pure two-qubit states. We present a complete solution to this long-lasting problem.
The study of quantum cryptography and quantum non-locality have traditionnally been based on two-level quantum systems (qubits). In this paper we consider a generalisation of Ekert's cryptographic protocol [Ekert] where qubits are replaced by qutrits. The security of this protocol is related to non-locality, in analogy with Ekert's protocol. In order to study its robustness against the optimal individual attacks, we derive the information gained by a potential eavesdropper applying a cloning-based attack.
Although the Gaussian-noise assumption is widely adopted in the study of qubit decoherence, non-Gaussian noise sources, especially the strong discrete fluctuators, have been detected in many qubits. It remains an important task to further understand and mitigate the distinctive decoherence effect of the non-Gaussian noise. Here, we study the qubit dephasing caused by the non-Gaussian fluctuators, and predict a symmetry-breaking effect that is unique to the non-Gaussian noise. This broken symmetry results in an experimentally measurable mismatch between the extremum points of the dephasing rate…
The rapid development in designs and fabrication techniques of superconducting qubits has helped making coherence times of qubits longer. In the near future, however, the radiative decay of a qubit into its control line will be a fundamental limitation, imposing a trade-off between fast control and long lifetime of the qubit. In this work, we successfully break this trade-off by strongly coupling another superconducting qubit along the control line. This second qubit, which we call a Josephson quantum filter (JQF), prevents the qubit from emitting microwave photons and thus suppresses its rela…
A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topolo…
We demonstrate a pogo pin package for a superconducting quantum processor specifically designed with a nontrivial layout topology (e.g., a center qubit that cannot be accessed from the sides of the chip). Two experiments on two nominally identical superconducting quantum processors in pogo packages, which use commercially available parts and require modest machining tolerances, are performed at low temperature (10 mK) in a dilution refrigerator and both found to behave comparably to processors in standard planar packages with wirebonds where control and readout signals come in from the edges. …
We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky and Brandenburger: strong contextuality, logical contextuality, and probabilistic contextuality. We study n-qubit pure states. We conjecture that for more than 2 parties, all entangled states are logically contextual. We prove a number of results in support of this conjecture: (1) We show that all permutation-symmetric states are logically non-local. (2) We st…
Wheeler's {\it observer-participancy} and the related {\it it from bit} credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck's {\it dessins d'enfants} to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.
We study time dependence of exchange symmetry properties of Bell states when two qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of 0.5 at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states un…
It is argued that the Heisenberg picture of standard quantum mechanics does not save Einstein locality as claimed in Deutsch and Hayden (2000). In particular, the EPR-type correlations that DH obtain by comparing two qubits in a local manner are shown to exist before that comparison. In view of this result, the local comparison argument would appear to ineffective in supporting their locality claim.
We experimentally demonstrate optimal entanglement distillation from two forms of two-qubit mixed states under local filtering operations according to the constructive method intruduced by F. Verstraete et al. [Phys. Rev. A 64, 010101(R) (2001)]. In principle, our set-up can be easily applied to distilling entanglement from arbitrary two-qubit partially mixed states. We also test the violation of the Clauser-Horne-Shinmony-Holt (CHSH) inequality for the distilled state from the first form of mixed state to show its "hidden non-locality".
The observation of the non-local properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work, we investigate the robustness of the non-locality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing non-locality in terms of experimental noise parameters, and demonstrate the importance o…
