Quantum State Tomography Research Articles

Retraction Note: A single-qubit-based HSL color model for efficient quantum image security applications

Retraction Note: A single-qubit-based HSL color model for efficient quantum image security applications

The accelerating universe in a noncommutative analytically continued foliated quantum gravity

Abstract Based on an analytically continued Riemannian foliated quantum gravity super-Hamiltonian, known as branch cut quantum gravity (BCQG) we propose a novel approach to investigating the effects of noncommutative geometry on a minisuperspace of variables, influencing the acceleration behavior of the Universe’s wave function and the cosmic scale factor. Noncommutativity is introduced through a deformation of the conventional Poisson algebra, enhanced with a symplectic metric. The resulting symplectic manifold provides a natural setting that enables an isomorphism between canonically conjugate dual vector spaces, spanning the BCQG cosmic scale factor and its complementary quantum counterpart. Using this formulation, we describe the dynamic evolution of the Universe’s wave function, the cosmic scale factor, and its complementary quantum image. Our results strongly suggest that the noncommutative algebra induces late-time accelerated growth of the wave function, the Universe’s scale factor, and its complementary quantum counterpart, offering a new perspective on explaining the accelerating cosmic expansion rate and the inflationary period. In contrast to the inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, analytically continued non-commutative foliated quantum gravity captures short and long scales, driving the evolutionary dynamics of the Universe through a reconfiguration of the primordial cosmic content of matter and energy. This reconfiguration is encapsulated into a quantum field potential, which leads to the generation of relic gravitational waves, a topic for future investigation. Graphical representations and contour plots indicate a characteristic torsion (or twist) deformation of spacetime geometry. This result introduces new speculative elements regarding the reconfiguration of matter and energy as a driver of spacetime torsion deformation, generating relic gravitational waves and serving as an alternative topological mechanism for the Universe’s acceleration. However, these assumptions require further investigation.

Group frames via magic states with applications to SIC-POVMs and MUBs

We connect magic (non-stabilizer) states, symmetric informationally complete positive operator valued measures (SIC-POVMs), and mutually unbiased bases (MUBs) in the context of group frames, and study their interplay. Magic states are quantum resources in the stabilizer formalism of quantum computation. SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations, quantum state tomography, and quantum cryptography, etc. In this work, we study group frames constructed from some prominent magic states, and further investigate their applications. Our method exploits the orbit of discrete Heisenberg–Weyl group acting on an initial fiducial state. We quantify the distance of the group frames from SIC-POVMs and MUBs, respectively. As a simple corollary, we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states, analogous to the well-known SIC-POVM fiducial states. We present an intuitive and direct construction of MUB fiducial states via quantum T-gates, and demonstrate that for the qubit system, there are twelve MUB fiducial states, which coincide with the H-type magic states. We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation. We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.

Device-independent certification of desirable properties with a confidence interval

In the development of quantum technologies, a reliable means for characterizing quantum devices, be it a measurement device, a state-preparation device, or a transformation device, is crucial. However, the conventional approach based on, for example, quantum state tomography or process tomography relies on assumptions that are often not necessarily justifiable in a realistic experimental setting. Although the device-independent (DI) approach to this problem bypasses the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval (CI). To illustrate the versatility of these methods, we demonstrate how we can use them to certify—with finite data—the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we provide examples showing how the amount of certifiable negativity and fidelity scales with the number of trials and how many experimental trials one needs to certify a qutrit state space or the presence of genuine tripartite entanglement. Overall, we have found that the PBR protocol and the martingale-based protocol often offer similar performance, even though the latter does have to presuppose any witness (Bell-like inequality). In contrast, our findings also show that the performance of the martingale-based protocol may be severely affected by one’s choice of Bell-like inequality. Intriguingly, a Bell function useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.

Putting the Twist into Quantum Imaging

Putting the Twist into Quantum Imaging

Evidence of the Quantum Optical Nature of High-Harmonic Generation

High-harmonic generation is a light up-conversion process occurring in a strong laser field, leading to coherent bursts of extreme ultrashort broadband radiation [Lewenstein , Phys. Rev. A , 2117 (1994)]. As a new perspective, we propose that ultrafast strong-field electronic or photonic processes such as high-harmonic generation can potentially generate nonclassical states of light well before the decoherence of the system occurs [Gorlach , Nat. Commun. , 4598 (2020); Stammer ., Phys. Rev. Lett. , 123603 (2022)]. This could address fundamental challenges in quantum technology such as scalability, decoherence, or the generation of massively entangled states [Lewenstein , Luca Argenti Michael Chini, 27 (2024)]. Here, we report experimental evidence of the nonclassical nature of the harmonic emission in several semiconductors excited by a femtosecond infrared laser. By investigating single- and double-beam intensity cross-correlation [Loudon, Rep. Prog. Phys. , 913 (1980)], we measure characteristic nonclassical features in the single-photon statistics. We observe two-mode squeezing in the generated harmonic radiation, which depends on the laser intensity that governs the transition from super-Poissonian to Poissonian photon statistics. The measured violation of the Cauchy-Schwarz inequality realizes a direct test of multipartite entanglement in high-harmonic generation [Wasak, Phys. Rev. A , 033616 (2014)]. This result is supported by the theory of multimodal detection and the Hamiltonian from which the effective squeezing modes of the harmonics can be derived [Gonoskov , Phys. Rev. B , 125110 (2024); Christ New J. Phys. , 033027 (2011)]. With this work, we show experimentally that high-harmonic generation is a new quantum bosonic platform that intrinsically produces nonclassical states of light with unique features such as multipartite broadband entanglement or multimode squeezing. The source operates at room temperature, using standard semiconductors and a standard commercial fiber laser, opening up new routes for the quantum industry, such as optical quantum computing, communication, and imaging. Published by the American Physical Society 2024

Unveiling the nonclassicality within quasi-distribution representations through deep learning

Abstract To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the dynamical process nonclassicality characterized by the canonical Hamiltonian ensemble representation (CHER) and the nonclassicality of quantum states
characterized by the Wigner function. However, to construct a multivariate joint quasi-distribution function with negative values from experimental data is typically highly cumbersome. Here we propose a computational approach utilizing a deep generative model, processing three marginals, to construct the bivariate joint quasi-distribution functions. We first apply our model to tackle the
challenging problem of the CHERs, which lacks universal solutions, rendering the problem ground-truth (GT) deficient. To overcome the GT deficiency of the CHER problem, we design optimal synthetic datasets to train our model. While trained with synthetic data, the physics-informed optimization enables our model to capture the detrimental effect of the thermal fluctuations on nonclassicality, which cannot be obtained from any analytical solutions. This underscores the reliability of our approach. This approach also allows us to predict the Wigner functions subject to thermal noises. Our model predicts the Wigner functions with a prominent accuracy by processing three marginals of probability distributions. Our approach also provides a significant reduction of the experimental efforts of
constructing the Wigner functions of quantum states, giving rise to an efficient alternative way to realize the quantum state tomography.

Optical Time-Domain Quantum State Tomography on a Subcycle Scale

Following recent progress in the experimental application of electro-optic sampling to the detection of the quantum fluctuations of the electromagnetic-field ground state and ultrabroadband squeezed states on a subcycle scale, we propose an approach to elevate broadband electro-optic sampling from a spectroscopic method to a full quantum tomography scheme, able to reconstruct a free-space quantum state directly in the time domain. By combining two recently developed methods to theoretically describe quantum electro-optic sampling, we analytically relate the photon-count probability distribution of the electro-optic signal to a transformed phase-space quasiprobability distribution of the sampled quantum state as a function of the time delay between the sampled midinfrared pulsed state and an ultrabroadband near-infrared probe pulse. We catalog and analyze sources of noise and show that in quantum electro-optic sampling with an ultrabroadband probe pulse one can expect to observe thermalization due to entanglement breaking. Mitigation of the thermalization noise enables a tomographic reconstruction of broadband quantum states while granting access to its dynamics on a subcycle scale. Published by the American Physical Society 2024

Multi-hop Quantum Teleportation Based on HSES via GHZ-like States

Abstract Implementing quantum wireless multi-hop network communication is essential to improve the global quantum network system. In this paper, we employ eight-level GHZ states as quantum channels to realize multi-hop quantum communication, and utilize the logical relationship between the measurements of each node to derive the unitary operation performed by the end node. The Hierarchical Simultaneous Entanglement Switching (HSES) method is adopted, resulting in a significant reduction in the consumption of classical information compared to the multi-hop quantum teleportation (QT) based on general Simultaneous Entanglement Switching (SES). In addition, the proposed protocol is simulated on the IBM Quantum Experiment Platform (IBM QE). Then, the data obtained from the experiment is analyzed using quantum state tomography, which verifies the protocol's good fidelity and accuracy. Finally, by calculating fidelity, we analyze the impact of four different types of noise (phase-damping, amplitude-damping, phase-flip, and bit-flip noise) in this protocol.

Cavity-enhanced induced coherence without induced emission

This paper presents a theoretical study of the enhancement of Zou-Wang-Mandel (ZWM) interferometry through cavity-enhanced spontaneous parametric down-conversion (SPDC) processes producing frequency-entangled biphotons. The ZWM interferometry shows the capability to generate interference effects between single signal photons via indistinguishability between the entangled idler photons. This paper extends the foundational principles of ZWM interferometry by integrating cavity-enhanced SPDCs, aiming to narrow photon bandwidths for improved coherence and photon pair generation efficiency, which is critical for applications in quantum information technologies, quantum encryption, and quantum imaging. This work explores the theoretical implication of employing singly resonant optical parametric oscillators within the ZWM interferometer to produce narrow-band single photons. By combining cavity-enhanced SPDCs with ZWM interferometry, this study fills a gap in current theoretical proposals, offering significant advancements in quantum cryptography and network applications that require reliable, narrow-band single photons.

Broadband generation and tomography of non-Gaussian states for ultra-fast optical quantum processors

Quantum information processors benefit from high clock frequencies to fully harness quantum advantages before they are lost to decoherence. All-optical systems offer unique benefits due to their inherent 100-THz carrier frequency, enabling the development of THz-clock frequency processors. However, the bandwidth of quantum light sources and measurement devices has been limited to the MHz range, with nonclassical state generation rates in the kHz range. In this study, we demonstrated broadband generation and quantum tomography of non-Gaussian states using an optical parametric amplifier (OPA) as a squeezed light source and an optical phase-sensitive amplifier (PSA). Our system includes a 6-THz squeezed-light source, a 6-THz PSA, and a 66-GHz homodyne detector. We successfully generated non-Gaussian states at a 0.9 MHz rate with sub-nanosecond wave packets using a continuous-wave laser. The performance is currently limited by the jitter of superconducting detectors, restricting the usable bandwidth to 1 GHz. Our technique extends the bandwidth to GHz, potentially increasing non-Gaussian state generation rates for practical optical quantum processors using OPAs.

Regression of Concurrence via Local Unitary Invariants

Concurrence is a crucial entanglement measure in quantum theory used to describe the degree of entanglement between two or more qubits. Local unitary (LU) invariants can be employed to describe the relevant properties of quantum states. Compared to quantum state tomography, observing LU invariants can save substantial physical resources and reduce errors associated with tomography. In this paper, we use LU invariants as explanatory variables and employ methods such as multiple regression, tree models, and BP neural network models to fit the concurrence of 2-qubit quantum states. For pure states and Werner states, by analyzing the correlation between data, a functional formula for concurrence in terms of LU invariants is obtained. Additionally, for any two-qubit quantum states, the prediction accuracy for concurrence reaches 98.5%.

Improvements to Quantum Interior Point Method for Linear Optimization

Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major bottleneck is the inexactness of quantum Tomography to extract classical solutions from quantum states. In addition, QLSAs are sensitive to the condition number, and this sensitivity is exacerbated when the Newton systems arising in IPMs converge to a singular matrix. Recently, an Inexact Feasible Quantum IPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs. However, this method requires a large number of gates and qubits to be implemented. Here, we propose a new IF-QIPM using the normal equation system, which requires less number of gates and qubits. To mitigate the sensitivity to the condition number and other input data-related parameters, we use preconditioning coupled with iterative refinement to obtain better complexity. Finally, we demonstrate the effectiveness of our approach on IBM Qiskit simulators.

Characterization of Defocused Coherent Imaging Systems with Periodic Objects

Recent advancements in quantum and quantum-inspired imaging techniques have enabled high-resolution 3D imaging through photon correlations. These techniques exhibit reduced degradation of image resolution for out-of-focus samples compared to conventional methods (i.e., intensity-based incoherent imaging). A key advantage of these correlation-based approaches is their independence from the system numerical aperture (NA). Interestingly, both improved resolution of defocused images and NA-independent scaling are linked to the spatial coherence of light. This suggests that while correlation measurements exploit spatial coherence, they are not essential for achieving this imaging advantage. This discovery has led to the development of optical systems that achieve similar performance by using spatially coherent illumination and relying on intensity measurements: direct 3D imaging with NA-independent resolution was recently demonstrated in a correlation-free setup using LED light. Here, we explore the physics behind the enhanced performance of defocused coherent imaging, showing that it arises from the modification of the sample’s spatial harmonic content due to diffraction, unlike the blurring seen in conventional imaging. The results we present are crucial for understanding the implications of the physical differences between coherent and incoherent imaging, and are expected to pave the way for the practical application of the discovered phenomena.

Quantum Color Image Encryption: Dual Scrambling Scheme based on DNA Codec and Quantum Arnold Transform

Abstract In the field of Internet, image is of great significance to information transmission. Meanwhile, how to ensure and improve its security has become the focus of research in the world today. We combine DNA codec with Quantum Arnold Transform (QArT) to propose a new double encryption algorithm for quantum color images. to improve the security and robustness of image encryption.Firstly, we utilize the biological characteristics of DNA codecs to perform encoding and decoding operations on pixel color information in quantum color images, and achieve pixel-level diffusion. Secondly, we use QArT to scramble the position information of quantum images and use the operated image as the key matrix for quantum XOR operations. All quantum operations in this paper are reversible, so the decryption operation of the ciphertext image can be realized by the reverse operation of the encryption process. We conduct simulation experiments on encryption and decryption using three color images of ”Monkey”, ”Flower” and ”House”. The experimental results show that the peak value and correlation of the encrypted images on the histogram have good similarity, and the average NPCR of RGB three-channel is 99.61%, the average UACI is 33.41%, and the average information entropy is about 7.9992. In addition, the robustness of the proposed algorithm is verified by the simulation of noise interference in the actual scenario.

Quantum image encryption algorithm based on 3D-BNM chaotic map

Quantum image encryption algorithm based on 3D-BNM chaotic map

Experimental Sample-Efficient Quantum State Tomography via Parallel Measurements.

Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method inspired by quantum overlapping tomography [Phys. Rev. Lett. 124, 100401 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.100401], which utilizes parallel measurements (PQST). In contrast to LQST, PQST significantly reduces the number of measurements and offers more robustness against shot noise. Experimentally, we demonstrate the feasibility of PQST in a treelike superconducting qubit chip by designing high-efficiency circuits, preparing W states, ground states of Hamiltonians, and random states, and then reconstructing these density matrices using full quantum state tomography (FQST), LQST, and PQST. Our results show that PQST reduces measurement cost, achieving fidelities of 98.68% and 95.07% after measuring 75 and 99 observables for six-qubit and nine-qubit W states, respectively. Furthermore, thereconstruction of the largest density matrix of the 12-qubit W state is achieved with the similarity of 89.23% after just measuring 243 parallel observables, while 3^{12}=531 441 complete observables are needed for FQST. Consequently, PQST will be a useful tool for future tasks such as the reconstruction, characterization, benchmarking, and properties learning of states.

Learning Quantum States and Unitaries of Bounded Gate Complexity

While quantum state tomography is notoriously hard, most states hold little interest to practically minded tomographers. Given that states and unitaries appearing in nature are of bounded gate complexity, it is natural to ask if efficient learning becomes possible. In this work, we prove that to learn a state generated by a quantum circuit with G two-qubit gates to a small trace distance, a sample complexity scaling linearly in G is necessary and sufficient. We also prove that the optimal query complexity to learn a unitary generated by G gates to a small average-case error scales linearly in G. While sample-efficient learning can be achieved, we show that under reasonable cryptographic conjectures, the computational complexity for learning states and unitaries of gate complexity G must scale exponentially in G. We illustrate how these results establish fundamental limitations on the expressivity of quantum machine-learning models and provide new perspectives on no-free-lunch theorems in unitary learning. Together, our results answer how the complexity of learning quantum states and unitaries relate to the complexity of creating these states and unitaries. Published by the American Physical Society 2024

Quantum image encryption protocol for secure communication in healthcare networks

Quantum image encryption protocol for secure communication in healthcare networks

Scalable quantum detector tomography by high-performance computing

Abstract At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyze these systems at the relevant scales, in a manner consistent with quantum mechanics, is therefore critical to benchmarking performance and characterizing their operation. While classical computational approaches cannot perform like-for-like computations of quantum systems beyond a certain scale, classical high-performance computing (HPC) may nevertheless be useful for precisely these characterization and certification tasks. By developing open-source customized algorithms using high-performance computing, we perform quantum tomography on a megascale quantum photonic detector covering a Hilbert space of 106. This requires finding 108 elements of the matrix corresponding to the positive operator valued measure (POVM), the quantum description of the detector, and is achieved in minutes of computation time. Moreover, by exploiting the structure of the problem, we achieve highly efficient parallel scaling, paving the way for quantum objects up to a system size of 1012 elements to be reconstructed using this method. In general, this shows that a consistent quantum mechanical description of quantum phenomena is applicable at everyday scales. More concretely, this enables the reconstruction of large-scale quantum sources, processes and detectors used in computation and sampling tasks, which may be necessary to prove their nonclassical character or quantum computational advantage.