In this perspective we discuss verification of quantum devices in the context of specific examples formulated as proposed experiments. Our first example is verification of analog quantum simulators ...as Hamiltonian learning, where the input Hamiltonian as the design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses cross-device verification on the quantum level (i.e., by comparing quantum states prepared on different quantum devices). We focus in particular on protocols using randomized measurements, and we propose establishing a central data repository, where existing experimental devices and platforms can be compared. In our final example, we address verification of the output of a quantum device from a computer science perspective, addressing the question of how a user of a quantum processor can be certain of the correctness of its output, and propose minimal demonstrations on present-day devices.
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement ...purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.
Abstract
We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The
k
-th condition involves comparing moments of the partially transposed ...density operator up to order
k
. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.
Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of ...entanglement. We characterize here almost all LOCC transformations among pure multipartite multilevel states. Combined with the analogous results for qubit states shown by Gour et al. J. Math. Phys. (N.Y.) 58, 092204 (2017), this gives a characterization of almost all local transformations among multipartite pure states. We show that nontrivial LOCC transformations among generic, fully entangled, pure states are almost never possible. Thus, almost all multipartite states are isolated. They can neither be deterministically obtained from local-unitary-inequivalent (LU-inequivalent) states via local operations, nor can they be deterministically transformed to pure, fully entangled LU-inequivalent states. In order to derive this result, we prove a more general statement, namely, that, generically, a state possesses no nontrivial local symmetry. We discuss further consequences of this result for the characterization of optimal, probabilistic single-copy and probabilistic multicopy LOCC transformations and the characterization of LU-equivalence classes of multipartite pure states.
Abstract
The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for ...both theoretical and practical reasons. As LOCC has a highly intricate structure, sometimes the larger set of separable (SEP) maps is considered, which has a mathematically much simpler description. In the literature, mainly SEP maps consisting of invertible Kraus operators have been taken into account. In this paper we show that the consideration of those maps is not sufficient when deciding whether a state can be mapped to another via general SEP transformations. This is done by providing explicit examples of transformations among pure three- and five-qubit states, which are feasible via SEP maps containing singular Kraus operators, however, not possible via SEP maps containing solely regular Kraus operators. The key point that allows to construct the SEP maps is to introduce projective measurements that occur with probability zero on the input state. The fact that it is not sufficient to consider SEP maps composed out of regular Kraus operators even in the case of pure state transformations, also affects the results on LOCC transformations among pure states. However, we show that non-invertible Kraus operators do not help in state transformations under LOCC with finitely many rounds of classical communication, i.e. the necessary and sufficient condition for SEP transformations with invertible Kraus operators is still a necessary condition for convertibility under finite-round LOCC. Moreover, we show that the results on transformations via SEP that are not possible with LOCC (including infinitely many rounds of classical communication) presented in Hebenstreit
et al
2016
Phys. Rev. A
93
, 012339 are not affected.
Genome-scale metabolic models (GSMMs) offer a holistic view of biochemical reaction networks, enabling in-depth analyses of metabolism across species and tissues in multiple conditions. However, ...comparing GSMMs Against each other poses challenges as current dimensionality reduction algorithms or clustering methods lack mechanistic interpretability, and often rely on subjective assumptions. Here, we propose a new approach utilizing logisitic principal component analysis (LPCA) that efficiently clusters GSMMs while singling out mechanistic differences in terms of reactions and pathways that drive the categorization. We applied LPCA to multiple diverse datasets, including GSMMs of 222 Escherichia -strains, 343 budding yeasts ( Saccharomycotina ), 80 human tissues, and 2943 Firmicutes strains. Our findings demonstrate LPCA’s effectiveness in preserving microbial phylogenetic relationships and discerning human tissue-specific metabolic profiles, exhibiting comparable performance to traditional methods like t-distributed stochastic neighborhood embedding (t-SNE) and Jaccard coefficients. Moreover, the subsystems and associated reactions identified by LPCA align with existing knowledge, underscoring its reliability in dissecting GSMMs and uncovering the underlying drivers of separation.
The aggregation‐induced emission properties of tetraarylethenes (TAEs) have led to numerous applications in chemistry, biology, and materials science. Herein, we describe two fluorinated ...tetraarylethenes, which can be employed as universal tags for the synthesis of solid state luminogens. The tags are accessible in one or two steps from commercially available starting materials. Facile coupling reactions with ubiquitous substrates such as thiols, alcohols, amines, phosphines, aldehydes, and enamines allow preparing a wide range of TAE conjugates, including tagged amino acids, peptides, carbohydrates, steroids, and commercial polymers.
A simple method for the coupling of fluorinated tetraarylethens to a wide range of substrates is described. The approach allows converting amino acids, bioactive compounds, carbohydrates, steroids, and polymers in one step into solid state luminogens.
Plasmid DNA (pDNA) is a key biotechnological product whose importance became apparent in the last years due to its role as a raw material in the messenger ribonucleic acid (mRNA) vaccine ...manufacturing process. In pharmaceutical production processes, cells need to grow in the defined medium in order to guarantee the highest standards of quality and repeatability. However, often these requirements result in low product titer, productivity, and yield. In this study, we used constraint-based metabolic modeling to optimize the average volumetric productivity of pDNA production in a fed-batch process. We identified a set of 13 nutrients in the growth medium that are essential for cell growth but not for pDNA replication. When these nutrients are depleted in the medium, cell growth is stalled and pDNA production is increased, raising the specific and volumetric yield and productivity. To exploit this effect we designed a three-stage process (1. batch, 2. fed-batch with cell growth, 3. fed-batch without cell growth). The transition between stage 2 and 3 is induced by sulfate starvation. Its onset can be easily controlled via the initial concentration of sulfate in the medium. We validated the decoupling behavior of sulfate and assessed pDNA quality attributes (supercoiled pDNA content) in E. coli with lab-scale bioreactor cultivations. The results showed an increase in supercoiled pDNA to biomass yield by 33% and an increase of supercoiled pDNA volumetric productivity by 13 % upon limitation of sulfate. In conclusion, even for routinely manufactured biotechnological products such as pDNA, simple changes in the growth medium can significantly improve the yield and quality.
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study ...party-local Clifford (PLC) transformations among stabilizer states. These transformations arise as a physically motivated extension of local operations in quantum networks with access to bipartite entanglement between some of the nodes of the network. First, we show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation, which describes local Clifford transformations among graph states. Then, we introduce a mathematical framework to study PLC equivalence of stabilizer states, relating it to the classification of tuples of bilinear forms. This framework allows us to study decompositions of stabilizer states into tensor products of indecomposable ones, that is, decompositions into states from the entanglement generating set (EGS). While the EGS is finite up to
3
parties Bravyi et al., J. Math. Phys.
47
, 062106 (2006), we show that for
4
and more parties it is an infinite set, even when considering party-local unitary transformations. Moreover, we explicitly compute the EGS for
4
parties up to
10
qubits. Finally, we generalize the framework to qudit stabilizer states in prime dimensions not equal to
2
, which allows us to show that the decomposition of qudit stabilizer states into states from the EGS is unique.
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