Simple Qubit Research Articles

Secure and robust randomness with sequential quantum measurements

Quantum correlations between measurements of separated observers are crucial for applications like randomness generation and key distribution. Although device-independent security can be certified with minimal assumptions, current protocols have limited performance. Here, we exploit sequential measurements, defined with a precise temporal order, to enhance performance by reusing quantum states. We provide a geometric perspective and a general mathematical framework, analytically proving a Tsirelson-like boundary for sequential quantum correlations, which represents a trade-off in nonlocality shared by sequential users. This boundary is advantageous for secure quantum randomness generation, certifying maximum bits per state with one remote and two sequential parties, even if one sequential user shares no nonlocality. Our simple qubit protocol reaches this boundary, and numerical analysis shows improved robustness under realistic noise. A photonic implementation confirms feasibility and robustness. This study advances the understanding of sequential quantum correlations and offers insights for efficient device-independent protocols.

Refined symmetry-resolved Page curve and charged black holes* *Supported in part by the Natural Science Foundation of China (12035016, 12275275). It is also supported by the Beijing Natural Science Foundation (1222031) and the Innovative Projects of Science and Technology ( E2545BU210) at IHEP.

The Page curve plotted using the typical random state approximation is not applicable to a system with conserved quantities, such as the evaporation process of a charged black hole, during which the electric charge does not macroscopically radiate out with a uniform rate. In this context, the symmetry-resolved entanglement entropy may play a significant role in describing the entanglement structure of such a system. We attempt to impose constraints on microscopic quantum states to match the macroscopic phenomenon of charge radiation during black hole evaporation. Specifically, we consider a simple qubit system with conserved spin/charge serving as a toy model for the evaporation of charged black holes. We propose refined rules for selecting a random state with conserved quantities to simulate the distribution of charges during the different stages of evaporation and obtain refined Page curves that exhibit distinct features in contrast to the original Page curve. We find that the refined Page curve may have a different Page time and exhibit asymmetric behavior on both sides of the Page time. Such refined Page curves may provide a more realistic description for the entanglement between the charged black hole and radiation during the evaporation process.

Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity

In two recent works, we studied the symmetry resolved Rényi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically characterised. In this paper we extend this line of investigation by providing analytical and numerical evidence that a similar universal behavior arises for the symmetry resolved negativity. In particular, we compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. These are “fused” versions of the more traditionally used branch point twist fields and were introduced in a previous work. The use of twist operators allows us to perform the computation in an arbitrary number of spacial dimensions. We show that, in the large-volume limit, only the commutation relations between the twist operators and local fields matter, and computations reduce to a purely combinatorial problem. We address some specific issues regarding fermionic excitations, whose treatment requires the notion of partial time-reversal transformation, and we discuss the differences and analogies with their bosonic counterpart. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons as well as for a large variety of very different states, ranging from simple qubit states to the excited states of free quantum field theories. Our predictions are tested numerically on a 1D Fermi chain.

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess U(1) symmetry. The same formulae are found for simple qubit states.

On the Use of Total State Decompositions for the Study of Reduced Dynamics

The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a time-dependent completely positive trace preserving (CPTP) map. Here, we take into account an approach that is based on a decomposition of any possibly correlated bipartite state as a conical combination involving statistical operators on the environment and general linear operators on the system, which allows one to fix the reduced-system evolution via a finite set of time-dependent CPTP maps. In particular, we show that such a decomposition always exists, also for infinite dimensional Hilbert spaces, and that the number of resulting CPTP maps is bounded by the Schmidt rank of the initial global state. We further investigate the case where the CPTP maps are semigroups with generators in the Gorini-Kossakowski-Lindblad-Sudarshan form; for two simple qubit models, we identify the positivity domain defined by the initial states that are mapped into proper states at any time of the evolution fixed by the CPTP semigroups.

Engineering high-coherence superconducting qubits

Advances in materials science and engineering have played a central role in the development of classical computers and will undoubtedly be critical in propelling the maturation of quantum information technologies. In approaches to quantum computation based on superconducting circuits, as one goes from bulk materials to functional devices, amorphous films and non-equilibrium excitations — electronic and phononic — are introduced, leading to dissipation and fluctuations that limit the computational power of state-of-the-art qubits and processors. In this Review, the major sources of decoherence in superconducting qubits are identified through an exploration of seminal qubit and resonator experiments. The proposed microscopic mechanisms associated with these imperfections are summarized, and directions for future research are discussed. The trade-offs between simple qubit primitives based on a single Josephson tunnel junction and more complex designs that use additional circuit elements, or new junction modalities, to reduce sensitivity to local noise sources are discussed, particularly in the context of materials optimization strategies for each architecture. Superconducting qubits hold great promise for quantum computing, and recently there have been dramatic improvements in both coherence times and the power of quantum processors. This Review explores how the path forward involves balancing circuit complexity and materials perfection, eliminating defects while designing qubits with engineered noise resilience.

Causal unitary qubit model of black hole evaporation

A new simple qubit model of black hole evaporation is proposed. The model operates on four qubits and is defined in terms of quantum gates and a quantum circuit. The chief features of the model include explicit unitarity and (most notably) causality which is understood as the impossibility of the transfer of information from the interior of the black hole through its horizon. The corresponding von Neumann entanglement entropy yields a crude (four-qubit) approximation of the Page curve.

Hybrid Quantum Interferometer in Bifurcation Mode as a Latching Quantum Readout

We have developed a new type of magnetometer consisting of a Hybrid Quantum Interference Device (HyQUID) that is set in a bi-stable state. We demonstrate its operation in a latching mode that can be employed to measure small changes in the applied flux. The device can be used to probe the flux state of a superconducting circuit using straightforward electrical resistance measurements, making it suitable as a simple qubit readout with low back-action.

Gauge models of musical forces

Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal attraction based on SU(2) symmetry. This model comprises two earlier attempts, the phase model grounded on U(1) gauge symmetry, and the spatial deformation model derived from SO(2) gauge symmetry. In the neutral, force-free case both submodels agree and generate the same predictions as a simple qubit approach. However, there are several differences in the force-driven case. It is claimed that the deformation model gives a proper description of static tonal attraction. The full model combines the deformation model with the phase model through SU(2) gauge symmetry and unifies static and dynamic tonal attraction.

Dissipative generators, divisible dynamical maps, and the Kadison-Schwarz inequality

We introduce a concept of Kadison-Schwarz divisible dynamical maps. It turns out that it is a natural generalization of the well known CP-divisibility which characterizes quantum Markovian evolution. It is proved that Kadison-Schwarz divisible maps are fully characterized in terms of time-local dissipative generators. Simple qubit evolution illustrates the concept.

On super-resolution imaging as a multiparameter estimation problem

We consider the problem of characterizing the spatial extent of a composite light source using the super-resolution imaging technique based on mode demultiplexing when the centroid of the source is not known precisely. We show that the essential features of this problem can be mapped onto a simple qubit model for joint estimation of a phase shift and a dephasing strength.

Discrete dynamics and non-Markovianity

We study discrete quantum dynamics where a single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often, non-Markovian memory effects are attributed to structured environments, whereas, here, we take a more general approach within a discrete setting. In addition of controlling the structure of the environment, we are interested in how local unitaries on the open system allow the appearance and control of memory effects. Our first simple qubit model where local unitary is followed by dephasing illustrates how memory effects arise, despite having no structure in the environment the system is coupled with. We, then, elaborate on this observation by constructing a model for an open quantum walk where the unitary coin and transfer operation is augmented with the dephasing of the coin. The results demonstrate tha,t in the limit of strong dephasing within each evolution step, the combined coin-position open system always displays memory effects, and their quantities are independent of the structure of the environment. Our construction makes possible an experimentally realizable open quantum walk with photons exhibiting non-Markovian features.

Rapid Driven Reset of a Qubit Readout Resonator

Using a circuit QED device, we demonstrate a simple qubit measurement pulse shape that yields fast ring-up and ring-down of the readout resonator regardless of the qubit state. The pulse differs from a square pulse only by the inclusion of additional constant-amplitude segments designed to effect a rapid transition from one steady-state population to another. Using a Ramsey experiment performed shortly after the measurement pulse to quantify the residual population, we find that compared to a square pulse followed by a delay, this pulse shape reduces the timescale for cavity ring-down by more than twice the cavity time constant. At low drive powers, this performance is achieved using pulse parameters calculated from a linear cavity model; at higher powers, empirical optimization of the pulse parameters leads to similar performance.

Extending SDL and LMC complexity measures to quantum states

An extension of SDL (Shiner, Davison, Landsberg) and LMC (López-Ruiz, Mancini, Calbet) complexity measures is proposed for the quantum information context, considering that Von Neumann entropy is a natural disorder quantifier for quantum states. As a first example of application, the simple qubit was studied, presenting results similar to that obtained by applying SDL and LMC measures to a classical probability distribution. Then, for the Werner state, a mixture of Bell states, SDL and LMC measures were calculated, depending on the mixing factor γ, providing some conjectures concerning quantum systems.

Qubits from extra dimensions

We link the recently discovered black hole-qubit correspondence to the structure of extra dimensions. In particular we show that for toroidal compactifications of type IIB string theory simple qubit systems arise naturally from the geometrical data of the tori parametrized by the moduli. We also generalize the recently suggested idea of the attractor mechanism as a distillation procedure of GHZ-like entangled states on the event horizon, to moduli stabilization for flux attractors in F-theory compactifications on elliptically fibered Calabi-Yau four-folds. Finally using a simple example we show that the natural arena for qubits to show up is an embedded one within the realm of fermionic entanglement of quantum systems with indistinguishable constituents.

Graph-theoretic quantum system modelling for information/computation processing circuits

This paper introduces graph-theoretic quantum system modelling (GTQSM), which is facilitated by considering the fundamental unit of quantum computation and information, viz. a quantum bit or qubit as a basic building block. Unit directional vectors ‘ket 0’ and ‘ket 1’ constitute two distinct fundamental quantum across variable orthonormal basis vectors (for the Hilbert space) specifying the direction of propagation, as it were, of information (or computation data) while complementary fundamental quantum through (flow rate) variables specify probability parameters (or amplitudes) as surrogates for scalar quantum information measure (von Neumann entropy). Applications of GTQSM are presented for quantum information/computation processing circuits ranging from a simple qubit and superposition or product of two qubits through controlled NOT and Hadamard gate operations to a substantive case of 3-port, 5-stage circuit for quantum teleportation. An illustrative circuit for teleporting a qubit is modelled as a complex ‘system of systems’ resulting in four probable transfer function models. It has the potential of extending the applications of GTQSM further to systems at the higher end of complexity scale too. The key contribution of this paper lies in generalization or extension of the graph-theoretic system modelling framework, hitherto used for classical (mostly deterministic) systems, to quantum random systems. Further extension of the graph-theoretic system modelling framework to quantum field modelling is the subject of future work.

Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence

We derive a first order differential equation for the decoherence of an orbital angular momentum entangled biphoton state propagating through a turbulent atmosphere. The derivation is based on the distortion that orbital angular momentum states experience due to propagation through a thin sheet of turbulent atmosphere. This distortion is treated as an infinitesimal transformation leading to a first order differential equation, which we call an infinitesimal propagation equation. The equation is applied to a simple qubit case to show how the entanglement decays.

Preparation and entanglement purification of qubits through Zeno-like measurements

A novel method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provide us with useful and practical methods of state preparation.

Explaining Information Transfer in Quantum Teleportation

In this paper I introduce a new species of teleportation which I use to evaluate three explanations of information transfer in quantum teleportation. I will argue that two explanations fail to explain the “physical effect” of teleportation. I will also argue that that information transfer, understood as something more than simple qubit transfer, is not necessary for teleportation to occur.