Maximal coherence in a generic basis

Quantum measurement is a class of quantum channels that sends quantum states\nto classical states. We set up resource theories of quantum coherence and\nquantum entanglement for quantum measurements and find relations between them.\nFor this, we conceive a relative entropy type quantity to account for the\nquantum resources of quantum measurements. The quantum coherence of a quantum\nmeasurement can be converted into the entanglement in a bipartite quantum\nmeasurement through coherence-non generating transformations. Conversely, a\nquantum entanglement monotone of quantum measurements induces a quantum\ncoherence monotone of quantum measurement. Our results confirm that the\nunderstanding on the link between quantum coherence and quantum entanglement is\nvalid even for quantum measurements which do not generate any quantum resource.\n

We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence non-generating channels. We prove that the relative entropy of coherence is monotonically decreasing under the coherence non-generating channels, while the coherence of formation may increase under such channels. Interestingly, by combining mathematically the coherence of formation to the entanglement of formation, we show that the coherence of formation of a single-qubit is never increased by a coherence non-generating channel. This leads to the superadditivity property for the coherence increasing power of quantum channels, namely, while two channels can not increase coherence individually, they may increase the quantum coherence of a composed system. Further, we derive the general form of the rank-2 coherence non-generating qubit channels. Our results contribute to the resource theory of quantum coherence.

The recently established resource theory of quantum coherence allows for a quantitative understanding of the superposition principle, with applications reaching from quantum computing to quantum biology. While different quantifiers of coherence have been proposed in the literature, their efficient estimation in today’s experiments remains a challenge. Here, we introduce a collective measurement scheme for estimating the amount of coherence in quantum states, which requires entangled measurements on two copies of the state. As we show by numerical simulations, our scheme outperforms other estimation methods based on tomography or adaptive measurements, leading to a higher precision in a large parameter range for estimating established coherence quantifiers of qubit and qutrit states. We show that our method is accessible with today’s technology by implementing it experimentally with photons, finding a good agreement between experiment and theory.

Resource theory of quantum coherence originated like entanglement in quantum information theory. However, still now proper classification of quantum states is missing under coherence. In this work, we have provided a classification of states under local incoherent operations. We have succeeded in deriving the necessary and sufficient condition for which two pure multipartite states are equivalent under stochastic local incoherent operations and classical communications (SLICC) and local incoherent operations and classical communications (LICC). In particular, we have succeeded in characterizing three qubit pure states under SLICC. Our result reveals the existence of infinite number of SLICC inequivalent classes for three qubit systems.

Quantum measurements are crucial for extracting information from quantum systems, but they are error-prone due to hardware imperfections in near-term devices. Measurement errors can be mitigated through classical post-processing, based on the assumption of a classical noise model. However, the coherence of quantum measurements leads to unavoidable quantum noise that defies this assumption. In this work, we introduce a two-stage procedure to systematically tackle such quantum noise in measurements. The idea is intuitive: we first detect and then eliminate quantum noise. In the first stage, inspired by coherence witness in the resource theory of quantum coherence, we design an efficient method to detect quantum noise. It works by fitting the difference between two measurement statistics to the Fourier series, where the statistics are obtained using maximally coherent states with relative phase and maximally mixed states as inputs. The fitting coefficients quantitatively benchmark quantum noise. In the second stage, we design various methods to eliminate quantum noise, inspired by the Pauli twirling technique. They work by executing randomly sampled Pauli gates before the measurement device and conditionally flipping the measurement outcomes in such a way that the effective measurement device contains only classical noise. We numerically demonstrate the two-stage procedure’s feasibility on the Baidu Quantum Platform. Notably, the results reveal significant suppression of quantum noise in measurement devices and substantial enhancement in quantum computation accuracy. We highlight that the two-stage procedure complements existing measurement error mitigation techniques, and they together form a standard toolbox for manipulating measurement errors in near-term quantum devices.

We investigate the dynamics of quantum coherence of a system consisting of two interacting atoms coupling with a common cavity which is filled with a nonlinear Kerr-like medium, in the presence of intrinsic decoherence. It is shown that the stationary quantum coherence can arise in the system as the time approach to infinite. In particular, the amount of stationary quantum coherence can be enhanced by adjusting the Kerr interaction and dipole-dipole interaction. Furthermore, we also explore the influence of Kerr interaction and dipole-dipole interaction on the transfer of quantum information by a witness of the trace distance and find that the transferred information and stationary quantum information can be controlled by the Kerr interaction and dipole-dipole interaction.

Taking into account the dephasing process in the realistic atomic ensemble, we theoretically study the generation of atomic spin squeezing via atomic coherence induced by the coupling and probe fields. Using the Heisenberg–Langevin approach, we find that the perfect spin squeezing in the X component can be obtained while the coupling and probe fields produce the maximum coherence between the ground state sublevels 1 and 2. Moreover, the degree of atomic spin squeezing in the X component can be strengthened with the increasing atomic density and/or Rabi frequency of the mixing field. The theoretical results provide a proof-of-principle demonstration of generating the atomic spin squeezing via quantum coherence in the realistic atomic ensemble which may find potential applications in quantum information processing and quantum networks.

This special section of Journal of Physics B: Atomic, Molecular and Optical Physics (J. Phys. B) is a compilation of articles originating from the three-day international workshop entitled 'Theory of Quantum Gases and Quantum Coherence', held in June 2003 in Levico, Italy. The workshop follows on from the Salerno workshop held in 2002 (see J. Phys. B volume 34, issue 23). The articles presented in this special section highlight the interdisciplary nature of Bose–Einstein condensation, both experimental and theoretical, and some of the exciting progress being made in the field at the moment.We would like to thank all of the institutions and people who have supported the workshop. The European Science Foundation has provided substantial financial support through the programme 'Quantum Degenerate Dilute Systems: Bose–Einstein Condensation and Beyond (BEC2000+)'. Our gratitude goes especially to the steering committee of the BEC2000+ programme and to its chairman, Professor Dr Martin Wilkens. The Research and Development Centre for Bose–Einstein Condensation of the Istituto Nazionale di Fisica della Materia (BEC-INFM) has been another important source of financial support and for this we thank especially the Director of the centre, Professor Sandro Stringari. We would also like to thank the Dipartimento di Fisica of the Università di Trento for financial and logistic help.As this international workshop coincided with the ten-year anniversary of the first ever BEC conference, which was also held in Levico, we asked Professor Allan Griffin to write an introduction to this special section based on the talk he gave at the workshop. This introduction (the following article) gives a nice overview of the first ever conference and celebrates the progress in the field of BEC over the past ten years.

Theory of quantum gases and quantum coherence: the Salerno BEC workshop, 3-5 June 2001This special section of Journal of Physics B: Atomic, Molecular and Optical Physics (J. Phys. B) is a compilation of articles originating from the three dayInternational workshop `Theory of quantum gases and quantum coherence', heldearlier this year in Salerno, Italy. The workshop programme was a verysuccessful mixture of topics bringing together colleagues working in differentbut related areas of research centred about the physics of cold atoms and Bose-Einsteincondensation (BEC). It proved to be a very stimulating and interestingevent and the organizers would like to thank all of the participants of theworkshop and the contributors to this special collection of papers for theirenthusiasm and involvement.The workshop was very unusual both in its goals and its structure. The main aimwas to create an environment where young researchers in the theory of ultra-coldquantum gases could present and discuss the results of their studies, both withother young researchers and senior experts in the field, in an informal setting,allowing free criticisms and scientific exchanges. With this objective, thecomposition of the workshop consisted mainly of PhD students, Post-Doctoralfellows and young research assistants, as well as leading seniorscientists. An international advisory committee selected all of the youngspeakers and we would like to extend our thanks to the members of the committeefor their careful selection and support.Another objective of the workshop was to bring together researchers from suchdiverse areas as BEC, atom and quantum optics, statistical mechanics andcondensed matter physics and provide an opportunity for a fertile cross-breedingof ideas, methods and techniques. The workshop was divided into six different,and more or less homogenous, sessions. Each session was opened and directed bya leading senior scientist in the field of research under discussion. Thetopics covered during the workshop include microscopic theories of BEC, finitetemperature dynamics and critical behaviours, spin squeezing and coherenteffects, low dimensional physics, topological objects and exclusion statistics,stochastic methods and kinetic theories, Josephson-like effects and opticallattices, BEC on complex networks, equilibrium and dynamical properties andphase space analysis of trapped Fermi gases and correlation function analysis ofrecent experiments.The variety and integrated discussion on these topics is reflected in the paperspresented here in this collection. The papers stem from both oral and postercontributions presented at the workshop, as well as additional contributionsstimulated by the workshop. They include both topical reviews and originalresearch and have been peer reviewed to the usual high standard of J. Phys. B.We would like to take this opportunity to thank Professor Keith Burnett forsupporting this editorial enterprise and the J. Phys. B publishing team both formaking its realization possible and for the journal's constant and robustcommitment to the physics of quantum gases and fundamental quantum systems. Weare impressed and delighted by the continuing progress in this fascinating andrapidly growing new field of research in fundamental physics. The reactions tothis little experiment seem to have been largely positive and several colleagueshave suggested that the workshop formula should be repeated and extended in thefuture to include contributions by our fellow experimentalists as well astheoreticians. We thus hope to have a second edition of the workshop very soon,with more young (and not so young!) scientists telling us about their new andexciting discoveries.Finally we would like to thank all of the institutions and people who havesupported the workshop. The European Science Foundation has providedsubstantial financial support throughout the programme `Quantum DegenerateDilute Systems: Bose-Einstein Condensation and Beyond (BEC 2000+)'. Ourgratitude goes especially to the steering committee of the BEC2000+ programmeand to its chairman, Professor Dr Martin Wilkens. The Italian IstitutoNazionale per la Fisica della Materia (INFM) has been another important sourceof financial support and for this we thank especially the Director of the INFMunit in Salerno, Professor Gianni Costabile. Last but not least we gratefullythank the Faculty of Science, the Department of Physics `E R Caianiello' ofthe University of Salerno, and its Director, Professor Ferdinando Mancini, forproviding a very substantial fraction of the total financial support.

Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent to which quantum coherence is diminished depends both on the channel and the incoherent basis. Motivated by this, we propose a measure of nonclassicality of a quantum channel as the average quantum coherence of the state space after the channel acts on, minimized over all orthonormal basis sets of the state space. Utilizing the squared $l_1$-norm of coherence for the qubit channels, the minimization can be treated analytically and the proposed measure takes a closed form of expression. If we allow the channels to act locally on a maximally entangled state, the quantum correlation is diminished making the states more classical. We show that the extent to which quantum correlation is preserved under local action of the channel cannot exceed the quantumness of the underlying channel. We further apply our measure to the quantum teleportation protocol and show that a nonzero quantumness for the underlying channel provides a necessary condition to overcome the best classical protocols.

Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such as entanglement. Recently, Dale, Jennings, and Rudolph negated the question by showing that a randomness processing, quantum Bernoulli factory, using quantum coherence, is strictly more powerful than the one with classical mechanics. In this Letter, focusing on the same scenario, we propose a theoretical protocol that is classically impossible but can be implemented solely using quantum coherence without entanglement. We demonstrate the protocol by exploiting the high-fidelity quantum state preparation and measurement with a superconducting qubit in the circuit quantum electrodynamics architecture and a nearly quantum-limited parametric amplifier. Our experiment shows the advantage of using quantum coherence of a single qubit for information processing even when multipartite correlation is not present.

Quantum information systems are expected to exhibit superiority compared with their classical counterparts. This superiority arises from the quantum coherences present in these quantum systems, which are obviously absent in classical ones. To exploit such quantum coherences, it is essential to control the phase information in the quantum state. The phase is analogue in nature, rather than binary. This makes quantum information technology fundamentally different from our classical digital information technology. In this paper, we analyse error sources and illustrate how these errors must be managed for the system to achieve the required fidelity and a quantum superiority.This article is part of the themed issue 'Quantum technology for the 21st century'.

Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is generally nonincreasing under incoherent operations. In this paper, we analyse under which dynamical conditions the l 1-norm or the relative entropy of coherence can remain unchanged under strictly incoherent operations (freezing coherence). We provide a detailed analysis of their structure together with exact geometric conditions of freezing coherence. It reveals a remarkable feature: any strictly incoherent operation freezing coherence can be decomposed as a convex combination of unitary operations. This partially answers an open question named unitary decomposition of doubly-stochastic quantum operations [M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000)]. Based on this analysis, we also give a complete classification of coherent states from operational coherence theory. This builds the counterpart of entanglement classification under LOCC.

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.KeywordsHadamard matrixTradeRankMathematics Subject Classification (2010):05B2015B34

We study the quantum state discrimination problem under the minimum error (ME) strategy for a set of N pure equidistant states. These states are characterized by the property that the inner product between any pair of states is given by a unique complex number S. We provide the explicit form of the states and analyze their main structural properties. The optimal success probability for ME discrimination is evaluated as a function of the number of states, as well as the modulus and phase of the inner product S. Furthermore, we propose an experimental scheme for implementing the ME discrimination of equidistant states. We also investigate the quantum coherence consumed in the implementation of the minimum error discrimination of the equidistant states, which has an established operational interpretation as cryptographic randomness gain. As an application, we propose a quantum communication protocol in which Alice prepares and sends one of the equidistant states, while Bob applies the minimum error discrimination to extract the classical information encoded in the state. Finally, we discuss the optimal conditions under which the protocol achieves an optimal balance of classical correlations and quantum coherence, thereby ensuring effective information transfer and cryptographic security.