Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent coexistence criteria. The two most common classes of operations - Luders operations and conditional state preparators - are analyzed. It is shown that Luders operations are coexistent only under very restrictive conditions, when the associated effects are either proportional to each other, or disjoint.
This talk is a survey of the question of joint measurability of coexistent observables and its is based on the monograph Operational Quantum Physics [1] and on the papers [2,3,4].
Two quantum effects are considered coexistent if they can be measured together. It is known that commutativity and comparability are sufficient but not necessary for the coexistence of two effects. We unify those two conditions to a simple but more widely applicable sufficient condition.
We study coexistence of CV-QKD and 7 classical 12.5 Gbit/s on-off keying channels in WDM transmission over the C-band. We demonstrate key generation with a distilled secret key rate between 20 to 50 kbit/s in experiments running continuously over 24 hours.
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of…
Von Neumann's statistical theory of quantum measurement interprets the instantaneous quantum state and derives instantaneous classical variables. In realty, quantum states and classical variables coexist and can influence each other in a time-continuous way. This has been motivating investigations since longtime in quite different fields from quantum cosmology to optics as well as in foundations. Different theories (mean-field, Bohm, decoherence, dynamical collapse, continuous measurement, hybrid dynamics, e.t.c.) emerged for what I call `coexistence of classical continuum with quantum'. I app…
The coexistence between Quantum Mechanics and Special Relativity is usually formulated in terms of the no-signaling condition. Several authors have even suggested that this condition should be included between the basic postulates of Quantum Theory. However, there are several scenarios where signaling is, in principle, possible: based on previous results and the analysis of the relation between unitarity and signaling we present an example of a two-particle interferometric arrangement for which the dynamics is, in principle, compatible with superluminal transmission of information. This type o…
Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State
Faculty of Physics, VNU University of Science, Vietnam National University（越南国立大学科学大学物理学院）；Institute for Quantum Technologies, Technology and Innovation Park, VNU Hanoi（河内越南国立大学科技园量子技术研究所）
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability are employed to analyze the possibility of measuring together two general quantum observables, characterizing different degrees of compatibility between measurements. It is known that two jointly measurable observables are always coexistent, and that the converse holds for various classes of observables, including the case of observables with two outcomes. He…
Quantum key distribution (QKD) uniquely allows distribution of cryptographic keys with security verified by quantum mechanical limits. Both protocol execution and subsequent applications require the assistance of classical data communication channels. While using separate fibers is one option, it is economically more viable if data and quantum signals are simultaneously transmitted through a single fiber. However, noise-photon contamination arising from the intense data signal has severely restricted both the QKD distances and secure key rates. Here, we exploit a novel temporal-filtering effec…
From Classical Stochastic to Monitored Quantum Dynamics: Dynamical Phase Coexistence in East Circuit Models
Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学技术中心）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（诺丁汉大学物理与天文学院及量子非平衡系统数学与理论物理中心）
We show that a rank-1 quantum observable (POVM) M is jointly measurable with a quantum observable M' exactly when M' is a smearing of M. If M is extreme, rank-1 and discrete then M and M' are coexistent if and only if they are jointly measurable.
Can there be `peaceful coexistence' between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit (i.e. the false assumption) in proofs of Bell inequalities as Outcome Independence would secure such peaceful coexistence: or, if not secure it, at least show a way---maybe the best or only way---to secure it. In this paper, I begin by being sceptical of Shimony's approach, urging that we need a relativistic solution to the quantum measurement problem (Section 2). Then I analyse Outcome Independence in Kent's realist one-world Lorentz-invariant interpret…
Accurate and Effective Model for Coexistence of Classical and Quantum Signals In Optical Fibers
University of L’Aquila（拉奎拉大学）；Eindhoven University of Technology（埃因霍温理工大学）；Nokia Bell Labs（诺基亚贝尔实验室）；Università Degli Studi di Parma（帕尔马大学）；Shanghai Jiao Tong University（上海交通大学）
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical consistency of the resulting models of stable quantum systems requires a reconstruction of an alternative, amended, physical inner product of states. We point out the less known fact that for more than one observable the task is not always feasible. The difficulty is re-analyzed and its elementary linear-algebraic interpretation and treatment are outlined.
A Quantum Phase Transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, that is briefly discussed, presents a second order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules-atoms in coexistence in the other one. Usual markers for this phase transition are the ground state energy and the expectation value of the number of atoms (or, alternatvely, the number of molecules) in the ground state. In this work, ot…
Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme observables and study relationships between coexistence, joint measurability, and post-processing of quantum observables when an extreme observable is involved. We also discuss another notion of compatibility and provide a counterexample separating this from the former notions.
We demonstrate for the first time the coexistence of a quantum-channel and 8x200 Gpbs 16-QAM optical channels with launching powers as high as -9dBm per channel in a 2 km HC-NANF. Comparative analysis with single-mode fibre reveals that the quantum channel could not be sustained at such power levels.
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of sel…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more detailed structure. W introduce sequential products of effect and operations. Although these have already been studied, we introduce the new concept of sequential products of effects with operations and operations with effects. We then consider various special types of operations. After developing properties of these concepts, the results are generalized to includ…
The feasibility of coexisting a quantum channel with carrier-grade classical optical channels over Hollow Core Nested Antiresonant Nodeless Fibre (HC-NANF) is experimentally explored for the first time in terms of achievable quantum bit error rate (QBER), secret key rate (SKR) as well as classical signal bit error rates (BER). A coexistence transmission of 1.6 Tbps is achieved for the classical channels simultaneously with a quantum channel over a 2 km-long HC-NANF with a total coexistence power of 0 dBm. To find the best and worst wavelength position for the classical channels, we simulated d…
Quantum key distribution (QKD) provides information-theoretic security based on the laws of quantum mechanics. The desire to reduce costs and increase robustness in real-world applications has motivated the study of coexistence between QKD and intense classical data traffic in a single fiber. Previous works on coexistence in metropolitan areas have used wavelength-division multiplexing, however, coexistence in backbone fiber networks remains a great experimental challenge, as Tbps data of up to 20 dBm optical power is transferred, and much more noise is generated for QKD. Here we present for t…
According to Relational Quantum Mechanics (RQM) the wave function $ψ$ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, $ψ$ is defined as a computational device encoding observers' information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of an underlying reality described by some ontic state. In this paper we argue that RQ…
The binodal of a boson square-well fluid is determined as a function of the particle mass through the newly devised quantum Gibbs ensemble Monte Carlo algorithm [R. Fantoni and S. Moroni, {\sl to be published}]. In the infinite mass limit we recover the classical result. As the particle mass decreases the gas-liquid critical point moves at lower temperatures. We explicitely study the case of a quantum delocalization de Boer parameter close to the one of $\mbox{}^4$He. For comparison we also determine the gas-liquid coexistence curve of $\mbox{}^4$He for which we are able to observe the binodal…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum circuits. Its realization in different quantum states is a focus research topic in both quantum computation and quantum matter. However, the proved realizations are subject to the paradigm of topological order (including its extensions), i.e. via a quantum code structure with macroscopic code distance. Here, we broaden the knowledge of long-range entangled states…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of coexistent pairs is known. We generalize the qubit coexistence characterization to all pairs of effects in arbitrary dimension that belong to the von Neumann algebra generated by two projections. We demonstrate the presented mathematical machinery by several examples, and show that it covers physically relevant classes of effect pairs.
Coexistence of long- and quasi-long range spatial order in 1D quantum quasicrystals
Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute for Quantum Electronics, Eidgenossische Technische Hochschule Zurich（苏黎世联邦理工学院量子电子学研究所）；Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg（奥格斯堡大学物理系电子关联与磁性理论物理第三研究所）
Large deviations and conditioned monitored quantum systems: a tensor network approach
Max-Plank-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理系与集成量子科学与工程中心）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（诺丁汉大学物理与天文学学院及量子非平衡系统数学与理论物理中心）
Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e. simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N >= 4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of indi…
