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We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that any quantum channel mapping states on some input Hilbert space $\mathrm{A}$ to states on some output Hilbert space $\mathrm{B}$ can be compressed into one with order $d\log d$ Kraus operators, where $d=\max(|\mathrm{A}|,|\mathrm{B}|)$, hence much less than $|\mathrm{A}||\mathrm{B}|$. In the case where the channel's outputs are all very mixed, this can be improved to order $d$. We discuss the optimality of this result as well as some consequences.

Interactions between seals and commercial fisheries can pose a significant threat to the conservation status of seal populations. In the Falkland Islands, home to over 50 % of the global South American fur seal (SAFS) population, there has been a dramatic (∼ 900 %) increase in the number of SAFS-fishery interactions in recent years. However, significant knowledge gaps regarding SAFS spatiotemporal foraging behaviour and habitat use hinders our capacity to assess the ecological mechanisms underpinning these interactions. In this study, we investigate the spatial overlap between SAFS foraging effort and commercial squid and finfish trawl fisheries in the Falkland Island Exclusive Economic Zone (EEZ). By spatially integrating two years of SAFS horizontal and vertical movement data with contemporaneous trawl-by-trawl information from the Falkland Islands fishing fleet, we examine whether SAFS concentrate their foraging effort in areas associated with greater squid and finfish catch quantities. Our findings reveal a marked spatial overlap between SAFS foraging effort and commercial trawling activity within the Falkland Islands EEZ, particularly in areas associated with Patagonian longfin squid (Doryteuthis gahi) and common hake (Merluccius hubbsi). Across the various metrics of foraging effort (summarised dive activity) examined, we found SAFS performed a greater number of dives, travelled greater vertical distances and performed deeper dives in intensively fished areas. These results suggest SAFS forage in the same habitats targeted by commercial squid and finfish fisheries, where they compete for demersal resources by performing a high frequency of deep dives. The implications of our findings are discussed within the broader context of local prey-field dynamics and fisheries-management. This study represents one of the most comprehensive investigations of SAFS movement ecology and advances our understanding of seal-fishery interactions in the Falkland Islands EEZ – a topic of increasing management concern. Importantly, this work can support conservation efforts for this globally significant SAFS population and contribute to long-term marine management objectives of the Falkland Islands fishery.

Abstract Background Intraoperative blood salvage (IBS) is regarded as an alternative to allogeneic blood transfusion excluding the risks associated with allogeneic blood. Currently, IBS is generally avoided in tumor surgeries due to concern for potential metastasis caused by residual tumor cells in the erythrocyte concentrate. Methods The feasibility, efficacy and safety aspects of the new developed Catuvab procedure using the bispecific trifunctional antibody Catumaxomab was investigated in an ex-vivo pilot study in order to remove residual EpCAM positive tumor cells from the autologous erythrocyte concentrates (EC) from various cancer patients, generated by a IBS device. Results Tumor cells in intraoperative blood were detected in 10 of 16 patient samples in the range of 69–2.6 × 105 but no residual malignant cells in the final erythrocyte concentrates after Catuvab procedure. IL-6 and IL-8 as pro-inflammatory cytokines released during surgery, were lowered in mean 28-fold and 52-fold during the Catuvab procedure, respectively, whereas Catumaxomab antibody was detected in 8 of 16 of the final EC products at a considerable decreased and uncritical residual amount (37 ng in mean). Conclusion The preliminary study results indicate efficacy and feasibility of the new medical device Catuvab allowing potentially the reinfusion of autologous erythrocyte concentrates (EC) produced by IBS device during oncological high blood loss surgery. An open-label, multicenter clinical study on the removal of EpCAM-positive tumor cells from blood collected during tumor surgery using the Catuvab device is initiated to validate these encouraging results.

A tridentate bis-NHC Pd complex, based on caffeine, was studied for its catalytic activity. This complex displayed a high catalytic activity in the Suzuki–Miyaura and Mizoroki–Heck cross-coupling reactions of aryl halides. The Sonogashira cross-coupling was also investigated but reveals a fast plateauing of the reaction. Aryl iodides as well as aryl bromides react when equipped with either electron-donating or electron-withdrawing substituents. Aryl chlorides, which contained electron-withdrawing groups, were also reactive under the applied conditions.

Data were combined from surveys in 2013, 2018, 2019 and 2021 to examine biomass changes of the skate (Rajiformes) stock in waters around the Falkland Islands. The 2013 and 2019 surveys were research surveys for skate abundance and used 90 mm trawl mesh to capture species and size compositions. The 2018 survey was a mesh size trial, and the 2021 survey was a commercial exploration; both used 400 mm trawl mesh to target skates. All four surveys were compared for biomass by deselecting the proportions of skates per size interval caught in 90 mm mesh that would not have been caught in 400 mm mesh, calculated with the SELECT method. Estimated commercial-size skate biomass decreased for most species individually and approximately 61% overall. Estimated commercial-size skate biomass also decreased by as much south of 51° latitude, the area that was closed to skate target fishing since 1996, as north of 51° latitude, which has been maintained open to skate target fishing. The outcome is correlated with continuing skate bycatch in finfish trawls.

The electrochemistry and photophysics of the Pt(II) complexes [Pt(naphen)(X)] (Hnaphen = naphtho[1,2-b][1,10]phenanthroline, X = Cl or C≡CPh) containing the rigid tridentate C^N^N-coordinating pericyclic naphen ligand was studied alongside the complexes of the tetrahydro-derivative [Pt(thnaphen)(X)] (Hthnaphen = 5,6,8,9-tetrahydro-naphtho[1,2-b][1,10]phenanthroline) and the N^C^N-coordinated complex [Pt(bdq)(Cl)] (Hbdq = benzo[1,2-h:5,4-h’]diquinoline. The cyclic voltammetry showed reversible reductions for the C^N^N complexes, with markedly fewer negative potentials (around −1.6 V vs. ferrocene) for the complexes containing the naphen ligand compared with the thnaphen derivatives (around −1.9 V). With irreversible oxidations at around +0.3 V for all of the complexes, the naphen made a difference in the electrochemical gap of about 0.3 eV (1.9 vs. 2.2 eV) compared with thnaphen. The bdq complex was completely different, with an irreversible reduction at around −2 V caused by the N^C^N coordination pattern, which lacked a good electron acceptor such as the phenanthroline unit in the C^N^N ligand naphen. Long-wavelength UV-Vis absorption bands were found around 520 to 530 nm for the C^N^N complexes with the C≡CPh coligand and were red-shifted when compared with the Cl derivatives. The N^C^N-coordinated bdq complex was markedly blue-shifted (493 nm). The steady-state photoluminescence spectra showed poorly structured emission bands peaking at around 630 nm for the two naphen complexes and 570 nm for the thnaphen derivatives. The bdq complex showed a pronounced vibrational structure and an emission maximum at 586 nm. Assuming mixed 3LC/3MLCT excited states, the vibronic progression for the N^C^N bdq complex indicated a higher LC character than assumed for the C^N^N-coordinated naphen and thnaphen complexes. The blue-shift was a result of the different N^C^N vs. C^N^N coordination. The photoluminescence lifetimes and quantum yields ΦL massively increased from solutions at 298 K (0.06 to 0.24) to glassy frozen matrices at 77 K (0.80 to 0.95). The nanosecond time-resolved study on [Pt(naphen)(Cl)] showed a phosphorescence emission signal originating from the mixed 3LC/3MLCT with an emission lifetime of around 3 µs.

N-Heterocyclic carbenes (NHCs) have seen more and more use over the years. The go-to systems that are usually considered are derivatives of benzimidazole or imidazole. Caffeine possesses an imidazole unit and was already utilized as a carbene-type ligand; however, its use within a tridentate bis-NHC system has—to the best of our knowledge—not been reported so far. The synthesis of the ligand is straightforward and metal complexes are readily available via silver-salt metathesis. A platinum(II) and a palladium(II) complex were isolated and a crystal structure of the former was examined. For the Pt(II) complex, luminescence is observed in solid state as well as in solution.

Magic (nonstabilizerness) is a necessary but “expensive” kind of “fuel” to drive universal fault-tolerant quantum computation. To properly study and characterize the origin of quantum “complexity” in computation as well as physics, it is crucial to develop a rigorous understanding of the quantification of magic. Previous studies of magic mostly focused on small systems and largely relied on the discrete Wigner formalism (which is only well behaved in odd prime power dimensions). Here we present an initiatory study of the magic of genuinely many-body quantum states that may be strongly entangled, with focus on the important case of many qubits, at a quantitative level. We first address the basic question of how “magical” a many-body state can be, and show that the maximum magic of an n-qubit state is essentially n, simultaneously for a range of “good” magic measures. As a corollary, the resource theory of magic has asymptotic golden currency states. We then show that, in fact, almost all n-qubit pure states have magic of nearly n. In the quest for explicit, scalable cases of highly entangled states whose magic can be understood, we connect the magic of hypergraph states with the second-order nonlinearity of their underlying Boolean functions. Next, we go on and investigate many-body magic in practical and physical contexts. We first consider a variant of measurement-based quantum computation where the client is restricted to Pauli measurements, in which magic is a necessary feature of the initial “resource” state. We show that n-qubit states with nearly n magic, or indeed almost all states, cannot supply nontrivial speedups over classical computers. We then present an example of analyzing the magic of “natural” condensed matter systems of physical interest. We apply the Boolean function techniques to derive explicit bounds on the magic of certain representative two-dimensional symmetry-protected topological states, and comment on possible further connections between magic and the quantum complexity of phases of matter.

Nowadays, the study of metallopolymers is one of the fastest growing areas of polymer science. Metallopolymers have great potential for application in multiple technological and various biomedical processes. The macromolecules with the possibility of varying the number and type of metal ions along the entire length of the polymer chain are of particular interest. In this regard, this study presents results on two successfully synthesized homopolymers, random and block copolymers based on PMMA, containing ferrocene and terpyridine moieties in the side chain. Different architectures of copolymers may attribute interesting properties when creating complexes with various metal ions. A detailed hydrodynamic study of these structures was carried out, the consistency of hydrodynamic data was established using the concept of a hydrodynamic invariant, the absolute values of the molar masses of the studied objects were calculated, and the conformational parameters of macromolecules were determined. Using the Fixman–Stockmayer theory, the equilibrium rigidities of the studied systems were calculated and the relationship between the chemical structure and conformational characteristics was established. The studied copolymers can be attributed to the class of flexible-chain macromolecules. An increase in the equilibrium rigidity value with an increase of the side chain, which is characteristic of comb-shaped polymers, was determined.

The contribution deals with the synthesis of the poly(methacrylate)-based copolymers, which contain ferrocene and/or terpyridine moieties in the side chains, and the subsequent analysis of their self-assembly behavior upon supramolecular/coordination interactions with Eu3+ and Pd2+ ions in dilute solutions. Both metal ions provoke intra and inter molecular complexation that results in the formation of large supra-macromolecular assembles of different conformation/shapes. By applying complementary analytical approaches (i.e., sedimentation-diffusion analysis in the analytical ultracentrifuge, dynamic light scattering, viscosity and density measurements, morphology studies by electron microscopy), a map of possible conformational states/shapes was drawn and the corresponding fundamental hydrodynamic and macromolecular characteristics of metallo-supramolecular assemblies at various ligand-to-ion molar concentration ratios (M/L) in extremely dilute polymer solutions (c[η]≈0.006) were determined. It was shown that intramolecular complexation is already detected at (L≈0.1), while at M/L>0.5 solution/suspension precipitates. Extreme aggregation/agglomeration behavior of such dilute polymer solutions at relatively “high” metal ion content is explained from the perspective of polymer-solvent and charge interactions that will accompany the intramolecular complexation due to the coordination interactions.

In presence of inter-system correlations, violations of the laws of thermodynamics become possible. Here, the authors develop a formalism redefining heat, work and thermodynamic laws in terms of quantum conditional entropy, which consistently generalize thermodynamics in correlated scenarios.

Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical information that could conflict with thermalisation. Here, we examine the overlap between thermal and objective states. We find that in general, one cannot exist when the other is present. However, there are certain regimes where thermality and objectivity are more likely to coexist: in the high temperature limit, at the non-degenerate low temperature limit, and when the environment is large. This is consistent with our experiences that everyday-sized objects can be both thermal and objective.

Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics. This tutorial focuses on the derivation of the first and second law for isolated and open quantum systems far from equilibrium, where such foundational questions also become practically relevant for emergent nanotechnologies. The derivation is based on a microscopic definition of five essential quantities: internal energy, thermodynamic entropy, work, heat, and temperature. These definitions are shown to satisfy the phenomenological laws of nonequilibrium thermodynamics for a large class of states and processes. The consistency with previous results is demonstrated. The framework applies to multiple baths including particle transport and accounts for processes with, e.g., a changing temperature of the bath, which is determined microscopically. An integral fluctuation theorem for entropy production is satisfied. In summary, this tutorial introduces a consistent and versatile framework to understand and apply the laws of thermodynamics in the quantum regime and beyond.

A universal programmable quantum processor uses “program” quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain “replication lemma” for unitaries.

A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's $\textit{No-Programming Theorem}$), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via $\textit{teleportation simulation}$, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.

A central concept in thermodynamics is the thermal state, which is the one towards which the system relaxes. Here, the authors derive the same state, through three different approaches, in the case of a quantum system whose conserved quantities correspond to operators that do not commute with one another.

It is by now well established that there exist nonlocal games for which the best entanglement-assisted performance is not better than the best classical performance. Here we show in contrast that any two-player XOR game, for which the corresponding Bell inequality is tight, has a quantum advantage. In geometric terms, this means that any correlation Bell inequality for which the classical and quantum maximum values coincide, does not define a facet, i.e., a face of maximum dimension, of the local (Bell) polytope. Indeed, using semidefinite programming duality, we prove upper bounds on the dimension of these faces, bounding it far away from the maximum. In the special case of nonlocal computation games, it had been shown before that they are not facet defining; our result generalizes and improves this. As a by-product of our analysis, we find a similar upper bound on the dimension of the faces of the convex body of quantum correlation matrices, showing that (except for the trivial ones expressing the non-negativity of probability) it does not have facets.

In this paper, we introduce intrinsic non-locality and quantum intrinsic non-locality as quantifiers for Bell non-locality, and we prove that they satisfy certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation p , while quantum intrinsic non-locality is an upper bound on the same capacity for a correlation arising from an underlying quantum model. We also prove that intrinsic steerability is faithful, and it is an upper bound on the secret-key-agreement capacity of any one-sided-device-independent protocol conducted using a device characterized by an assemblage $\hat{\rho }$ . Finally, we prove that quantum intrinsic non-locality is bounded from above by intrinsic steerability.

Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that $\textit{information is physical}$ - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations. Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a $\textit{completely passive}$ state, acquires Boltzmann-Gibbs canonical form with an $\textit{intrinsic temperature}$. We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our $\textit{intrinsic temperature}$ based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.

Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel-which reduces to the homonymous measure for states when computed on constant-output channels-and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that every pure coherent state in dimension larger than $2$, however weakly so, turns out to be a valuable resource to implement some coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation at the phase space level; and (b) Gaussian dilatable channels, that admit a Stinespring dilation involving a Gaussian unitary. Our main result is that the set (a) coincides with the closure of (b) with respect to the strong operator topology. We also present an example of a channel in (a) which is not in (b), implying that taking the closure is in general necessary. This provides a complete resolution to the conjecture posed in Sabapathy and Winter (2017 Phys. Rev. A 95 062309). Our proof technique is constructive, and yields an explicit procedure to approximate a given linear bosonic channel by means of Gaussian dilations. It turns out that all linear bosonic channels can be approximated by a Gaussian dilation using an ancilla with the same number of modes as the system. We also provide an alternative dilation where the unitary is fixed in the approximating procedure. Our results apply to a wide range of physically relevant channels, including all Gaussian channels such as amplifiers, attenuators, phase conjugators, and also non-Gaussian channels such as additive noise channels and photon-added Gaussian channels. The method also provides a clear demarcation of the role of Gaussian and non-Gaussian resources in the context of linear bosonic channels. Finally, we also obtain independent proofs of classical results such as the quantum Bochner theorem, and develop some tools to deal with convergence of sequences of quantum channels on continuous variable systems that may be of independent interest.

We address the problem of understanding, from first principles, the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand, previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight since particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, are unrealistically short. However, most physically relevant situations fall outside these two classes. In this paper, we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.

We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-$Z$ and -$X$ bases. This strategy was recently shown to achieve an approximate unitary $2$-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process achieve decoupling at the same rate as that with the uniform ones, showing that rather imprecise approximations of unitary $2$-designs are sufficient for decoupling. We also briefly discuss efficient implementations of them and implications of our decoupling theorem to coherent state merging and relative thermalisation.

Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

In the crystal structure of the title compound, C17H12N4, the angle between the naphthalene and 1H-1,2,3-triazole ring systems is 71.02 (4)° and that between the pyridine and triazole rings is 8.30 (9)°.

Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this paradigmatic quantum effect in macroscopic high temperature systems is constrained by the limited access to the quantum state of the system. In this paper we show how macroscopic observables beyond the mean energy of the system can be exploited as proxy witnesses for entanglement detection. Using linear and semi-definite relaxations we show that all previous approaches to this problem can be outperformed by our proxies, i.e. entanglement can be certified at higher temperatures without access to any local observable. For an efficient computation of proxy witnesses one can resort to a generalised grand canonical ensemble, enabling entanglement certification even in complex systems with macroscopic particle numbers.