Search Results (13)

Quantum network correlations are crucial for long-distance quantum communication, quantum cryptography, and distributed quantum computing. Detecting network steering is particularly challenging in complex network structures. We have studied the steering inequality criteria for a 2-forked 3-layer tree-shaped network. Assuming the first and third layers are trusted and the second layer is untrusted, we derived a steering inequality criterion using the correlation matrix between trusted and untrusted observables. In particular, we apply the steering criterion to three classes of measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We further illustrate the effectiveness of our method through an example. Full article

In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information processing, our method is based on weak couplings and ancillary systems, eliminating the need for classical communication, optimization, and complex calculations. The concept of mutually unbiased bases is intrinsically linked to symmetry, as it entails the uniform distribution of quantum states across distinct bases. Within the framework of our theoretical model, mutually unbiased bases are employed to facilitate weak measurements and to function as the post-selected states. To quantify the correlations in the initial state, we employ the trace distance between the initial state and the product of its marginal states, and illustrate the feasibility and effectiveness of our approach. We generalize the approach to accommodate high-dimensional multi-particle systems for potential applications in quantum information processing and quantum networks. Full article

As an important branch of secure multi-party computation, privacy set intersection enables multiple parties to input their private sets and jointly compute the intersection of these sets without revealing any information other than the intersection itself. With the increasing demand for privacy protection of user data, privacy set intersection has been widely used in privacy computing and other fields. In this paper, we utilize the properties of mutually unbiased bases to propose a multi-party quantum private set intersection protocol that incorporates identity authentication mechanisms. A semi-honest third party (TP) is introduced to facilitate the secure execution of this task among the multiple participating parties. The TP establishes a shared master key with each party, which serves as the basis for authenticating the identity of each participant throughout the protocol. Single-particle quantum states, prepared by the TP, act as the information carriers and are sequentially transmitted among the participating parties. Each party performs a local unitary operation on the circulating particle, thereby encoding their private data within the quantum state. At the end of the protocol, the TP announces his measurement result, by which all participants can concurrently ascertain the intersection of their private data sets. Notably, the proposed protocol eliminates the need for long-term storage of single-particle quantum states, thereby rendering it feasible with existing quantum technological capabilities. Furthermore, a comprehensive security analysis demonstrates that the protocol effectively resists some common external and internal attacks, thereby ensuring its theoretical security. Full article

The development of holography has facilitated significant advancements across a wide range of disciplines. A phase-only spatial light modulator (SLM) plays a crucial role in realizing digital holography, typically requiring a phase mask as its input. Non-iterative (NI) algorithms are widely used for phase mask generation, yet they often fall short in delivering precise solutions and lack adaptability in complex scenarios. In contrast, the Simulated Annealing (SA) algorithm provides a global optimization approach capable of addressing these limitations. This study investigates the integration of NI algorithms with the SA algorithm to enhance the optimization of phase mask generation in digital holography. Furthermore, we examine how adjusting annealing parameters, especially the cooling strategy, can significantly improve system optimization performance and symmetry. Notably, we observe a considerable improvement in the efficiency of the SA algorithm when non-iterative methods are employed to generate the initial phase mask. Our method achieves a perfect representation of the symmetry in desired light fields. The efficacy of the optimized phase masks is evaluated through optical tomographic measurements using two-dimensional mutually unbiased bases (MUBs), with the resulting average similarity reaching 0.99. These findings validate the effectiveness of our methodin optimizing phase mask generation and underscore its potential for high-precision optical mode recognition and analysis. Full article

The achievable capacity index (ACI) is a simple and efficient approach for estimating the profitability of newsboy-type products, wherein profitability is defined as the probability of achieving the target profit by optimizing the order quantity. At present, the ACI is applicable to single retail stores (i.e., single demand) but not to multiple sales channels (i.e., multiple demand). This paper presents an integrated achievable capacity index (IACI) by which to measure the aggregate profitability of multiple mutually independent channels under normally distributed demand. An unbiased IACI estimator is also developed, to which is applied the Taylor expansion to approximate its sampling distribution, wherein the sizes, means, and variances of demand differ in each channel. Furthermore, overestimates due to sampling error are avoided by deriving the lower confidence bound for the IACI. This paper also provides generic tables to aid managers seeking conservative estimates of profitability. The applicability of the proposed scheme is demonstrated numerically using a real-world example involving an own-branding-and-manufacturing (OBM) enterprise with multiple owned channels. Full article

Quantum secret sharing (QSS) is an important branch of quantum cryptography. Identity authentication is a significant means to achieve information protection, which can effectively confirm the identity information of both communication parties. Due to the importance of information security, more and more communications require identity authentication. We propose a d-level $(t,n)$ threshold QSS scheme in which both sides of the communication use mutually unbiased bases for mutual identity authentication. In the secret recovery phase, the sharing of secrets that only the participant holds will not be disclosed or transmitted. Therefore, external eavesdroppers will not get any information about secrets at this phase. This protocol is more secure, effective, and practical. Security analysis shows that this scheme can effectively resist intercept–resend attacks, entangle–measure attacks, collusion attacks, and forgery attacks. Full article

Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function $m(e,f)$ of two orthonormal bases e and f, we investigate the relationships between sets $\mathcal{I}\left(e\right)$ and $\mathcal{I}\left(f\right)$ of incoherent states with respect to e and f. We prove that $\mathcal{I}\left(e\right)=\mathcal{I}\left(f\right)$ if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection $\mathcal{I}\left(e\right)\bigcap \mathcal{I}\left(f\right)$ to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set $\mathcal{B}$ of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to $\mathcal{B}$ when $k=2$ and it is not the case for $k=3$. Full article

Quantum entanglement is one of the essential resources in quantum information processing. It is of importance to verify whether a quantum state is entangled. At present, a typical quantum certification focused on the classical correlations has attracted widespread attention. Here, we experimentally investigate the relation between quantum entanglement and the classical complementary correlations based on the mutual information, Pearson correlation coefficient and mutual predictability of two-qubit states. Our experimental results show the classical correlations for complementary properties have strong resolution capability to verify entanglement for two qubit pure states and Werner states. We find that the resolution capability has great performance improvement when the eigenstates of the measurement observables constitute a complete set of mutually unbiased bases. For Werner states in particular, the classical complementary correlations based on the Pearson correlation coefficient and mutual predictability can provide the ultimate bounds to certify entanglement. Full article

Sea Surface Temperature (SST) is an essential climate variable (ECV) for monitoring the state and detecting changes in the climate. The concept of ECVs, developed by the Global Climate Observing System (GCOS) program of the World Meteorological Organization (WMO), has been broadly adopted in worldwide science and policy circles Besides being a climate change indicator, the global SST field is an essential input for atmospheric models, air-sea exchange studies, understanding marine ecosystems, operational weather, and ocean forecasting, military and defense operations, tourism, and fisheries research. It is, therefore, critical to understand the errors associated with SST measurements from both in situ measurements and satellite observations. The customary way of validating a satellite SST is to compare it with in situ measured SSTs. This method, however, will have inaccuracies due to uncertainties involving both types of measurements. A triple collocation (TC) error analysis can be implemented on three mutually independent error-prone measurements to estimate the root-mean-square error (RMSE) of each measurement. In this study, the error characterization for the Pathfinder SST version 5.3 (PF53) dataset is performed using an extended TC (ETC) method and reported to be in the range of 0.31 to 0.37 K. These values are reasonable, as is evident from corresponding very high (~0.98) unbiased signal-to-noise ratio (SNR) values. Full article

In this paper, the SOMOSTA (Soil Moisture Monitoring Station) experiment on the intercomparison of soil moisture monitoring from Global Navigation Satellite System Reflectometry (GNSS-R) signals and passive L-band microwave radiometer observations at the Valencia Anchor Station is introduced. The GNSS-R instrument has an up-looking antenna for receiving direct signals from satellites, and a dual-pol down-looking antenna for receiving LHCP (left-hand circular polarization) and RHCP (right-hand circular polarization) reflected signals from the soil surface. Data were collected from the three different antennas through the two channels of Oceanpal GNSS-R receiver and, in addition, calibration was performed to reduce the impact from the differing channels. Reflectivity was thus measured, and soil moisture could be retrieved. The ESA (European Space Agency)-funded ELBARA-II (ESA L Band Radiometer II) is an L-band radiometer with two channels with 11 MHz bandwidth and respective center frequencies of 1407.5 MHz and 1419.5 MHz. The ELBARAII antenna is a large dual-mode Picket horn that is 1.4 m wide, with a length of 2.7 m with −3 dB full beam width of 12° (±6° around the antenna main direction) and a gain of 23.5 dB. By comparing GNSS-R and ELBARA-II radiometer data, a high correlation was found between the LHCP reflectivity measured by GNSS-R and the horizontal/vertical reflectivity from the radiometer (with correlation coefficients ranging from 0.83 to 0.91). Neural net fitting was used for GNSS-R soil moisture inversion, and the RMSE (Root Mean Square Error) was 0.014 m³/m³. The determination coefficient between the retrieved soil moisture and in situ measurements was R² = 0.90 for Oceanpal and R² = 0.65 for Elbara II, and the ubRMSE (Unbiased RMSE) were 0.0128 and 0.0734 respectively. The soil moisture retrievals by both L-band remote sensing methods show good agreement with each other, and their mutual correspondence with in-situ measurements and with rainfall was also good. Full article

Suppose that a d-dimensional Hilbert space $\mathcal{H}\simeq {\mathbb{C}}^d$ admits a full set of mutually unbiased bases $\left\{|1^{\left(a\right)}\rangle ,,,\cdots ,,,|d^{\left(a\right)}\rangle \right\}$ , where $a=1,\cdots ,d+1$ . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on $\mathcal{H}$ through iterative applications of measurements $M^{\left(a\right)}=\left\{|1^{\left(a\right)}\rangle ,\langle 1^{\left(a\right)}|,,,\cdots ,,,|d^{\left(a\right)}\rangle ,\langle d^{\left(a\right)}|\right\}$ for $a=1,\cdots ,d+1$ , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography. Full article

An unexpected connection exists between compatibility criteria for quantum states and Symmetric Informationally Complete quantum measurements (SIC-POVMs). Beginning with Caves, Fuchs and Schack’s "Conditions for compatibility of quantum state assignments", I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way to understand the relationship between SIC-POVMs and mutually unbiased bases, as calculations in the SIC representation of quantum states make clear. This, in turn, illuminates the resources necessary for magic-state quantum computation, and why hidden-variable models fail to capture the vitality of quantum mechanics. Full article

Recently there has been much effort in the quantum information community to prove (or disprove) the existence of symmetric informationally complete (SIC) sets of quantum states in arbitrary finite dimension. This paper strengthens the urgency of this question by showing that if SIC-sets exist: (1) by a natural measure of orthonormality, they are as close to being an orthonormal basis for the space of density operators as possible; and (2) in prime dimensions, the standard construction for complete sets of mutually unbiased bases and Weyl-Heisenberg covariant SIC-sets are intimately related: The latter represent minimum uncertainty states for the former in the sense of Wootters and Sussman. Finally, we contribute to the question of existence by conjecturing a quadratic redundancy in the equations for Weyl-Heisenberg SIC-sets. Full article