Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common cause acting on both. Here, we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated upon observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.
We propose a methodology to emulate quantum phenomena arising from any non-classical quantum state using only a finite set of mixtures of coherent states. This allows us to successfully reproduce well-known quantum effects using resources that can be much more feasibly generated in the laboratory. We present a simple procedure to experimentally carry out quantum-state emulation with coherent states, illustrate it emulating multi-photon NOON states with few phase-averaged coherent states, and demonstrate its capabilities in observing fundamental quantum-mechanical effects, such as the Hong-Ou-M…
Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are however not captured by commonly used non-classicality measures. We identify a set of desired properties for any non-classicality measure that aims to capture these quantum features, and define the discord potential CD, which we show to satisfy all those properties. We compare the discord potential with recently proposed coherence monotones, and prove that the …
We study a two-species mixture of exciton-polaritons with self- and cross-interaction nonlinearities in a double well structure, in the presence of relaxation and continuous pumping. We identify the conditions that render the system parity-time ($\mathcal{PT}$) symmetric, and investigate its dynamic and static properties. We show that the system can exhibit long-term coherent oscillations of populations of the two polaritonic components between the two potential wells, and can simulate the dynamics of a pair of spin-1/2 particles (qubits) in the presence of exchange interaction.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e. using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number $N$ of channels with arbitrary individual capacity i.e. information preservation characteristics in the case of indefinite causal order. We pr…
We study two-component atomic gas mixtures in one dimension involving both bosons and fermions. When the inter-species interaction is attractive, we report a rich variety of coherent ground-state phases that vary with the intrinsic and relative strength of the interactions. We avoid any artifacts of lattice discretization by developing a novel implementation of a continuous matrix product state ansatz for mixtures and priorly demonstrate the validity of our approach on the integrable point that exists for mixtures with equal masses and interactions (Lai-Yang model) where we find that the ansat…
The relationship between thermal light and coherent pulses is of fundamental and practical interest. We now know that thermal light cannot be represented as a statistical mixture of single pulses. In this paper we ask whether or not thermal light can be represented as a statistical mixture of sets of pulses. We consider thermal light in a one-dimensional wave-guide, and find a convex decomposition into products of orthonormal coherent states of localized, nonmonochromatic modes.
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common cause, and each of these causal mechanisms can be coherent or not. Furthermore, one can combine these mechanisms in different ways: by probabilistically realizing either one or the other or by having both act simultaneously (termed a physical mixture). In the latter case, it is possible for the two mechanisms to be combined quantum-coherently. Previous work has…
First-order phase transition in atom-molecule quantum degenerate mixtures with coherent three-body recombination
Missouri University of Science and Technology（密苏里科技大学）；Ben-Gurion University of the Negev（内盖夫本古里安大学）；Harvard & Smithsonian（哈佛大学与史密森尼学会）；University of Chicago（芝加哥大学）
The constraints arising for a general set of causal relations, both classically and quantumly, are still poorly understood. As a step in exploring this question, we consider a coherently controlled superposition of "direct-cause" and "common-cause" relationships between two events. We propose an implementation involving the spatial superposition of a mass and general relativistic time dilation. Finally, we develop a computationally efficient method to distinguish such genuinely quantum causal structures from classical (incoherent) mixtures of causal structures and show how to design experiment…
We investigate the connection between thermal light and coherent pulses, constructing mixtures of single pulses that yield the same first-order, equal-space-point correlation function as thermal light. We present mixtures involving (i) pulses with a Gaussian lineshape and narrow bandwidths, and (ii) pulses with a coherence time that matches that of thermal light. We characterize the properties of the mixtures and pulses. Our results introduce an alternative description of thermal light in terms of multi-frequency coherent states, valid for the description of broadband linear light-matter inter…
Indefinite causal order with output-signalling instruments
Universidade Federal do Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；Technische Universität Wien（维也纳工业大学）；Università degli Studi di Pavia（帕维亚大学）
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the…
We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit $1/N$ can be beaten by the coherent superposition without the help of indefinite causal order. And in parameter estimation, we demonstrate that the strategy with the coherent superposition can perform better than the strategy with quantum \textsc{switch} which can generate indefinite causal order. We analytically obtain the general form of estimation precision in terms of the quantum Fisher information and further prove …
The replica method for calculating the von Neumann entropy is reviewed. Explicit expression for the entropy of the mixed coherent states $|α>$ and $|β>$ is obtained using this method. The purity inequality for bipartite system for separable states is studied on example of even and odd Schrödinger cat state.
Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as resources for concrete information-theoretic tasks. Here, we take a step forward by deriving a complete operational framework for causal nonseparability as a resource. Our first contribution is a formal definition of quantum control of causal orders, a stronger form of causal nonseparability (with the celebrated quantum switch as best-known example) where t…
In this paper, we show that it is possible to significantly boost the heat extraction ability of the ICO fridge by applying N identical thermalising channels in a superposition of N cyclic causal orders[2], and that this can be further boosted in the ultracold regime by replacing the working qubit with a quDit working substance. Moreover, we show that for the alternative controlled-SWAPs scheme presented in [1] where one additionally has access to the reservoir qubits which are quantum correlated with the control-target system, the performance can be greatly enhanced in general (tripled for al…
The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders. The causal relation between the laboratories is described by the process matrix. We show that, if the inputs of the laboratories are measured in a fixed basis, one can introduce an effective process matrix which is operationally indistinguishable from the original one. This effective process matrix can be obtained by applying the von Neumann- Luders update rul…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities --- just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical c…
In quantum mechanics events can happen in no definite causal order: in practice this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Indefinite causal order can be observed in a quantum switch, where two operations act in a quantum superposition of the two possible orders. Here we realise a photonic quantum switch, where polarisation coherently controls the order of two operations, $\hat{A}$ and $\hat{B}$, on the transverse spatial mode of the photons. Our setup avoids the limitations of earlier implementations: the operations …
The causal order of events need not be fixed: whether a bus arrives before or after another at a certain stop can depend on other variables -- like traffic. Coherent quantum control of causal order is possible too and is a useful resource for several tasks. However, quantum control implies that a controlling system carries the which-order information -- if the control is traced out, the order of events remains in a probabilistic mixture. Can the order of two events be in a pure superposition, uncorrelated with any other system? Here we show that this is not possible for a broad class of proces…
In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite causality. The mainstream view, that of "process matrices", takes a top-down approach to the problem, considering all causal correlations that are compatible with local quantum experiments. Conversely, we pursue a bottom-up approach, investigating how the concept of indefiniteness emerges from specific characteristics of generic operational theories. Specifically, w…
