Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g. towards a theory of quantum gravity---to the applied---e.g. for advantages in communication and computation. In this review, we will walk through the basic theory of indefinite causal order and focus on experiments that rely on a physically realisable indefinite causal ordered process---the quantum switch.
This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e., $f(UV)=f(U)f(V)$, it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., $f(UV)=f(V)f(U)$. In particular, we prove that when $f$ is an anti-homomorphism, sequential circuits could exponentially out…
Nordita, Stockholm University and KTH Royal Institute of Technology（诺尔迪塔，斯德哥尔摩大学和皇家理工学院）；School of Mathematics and Physics, The University of Queensland（昆士兰大学数学与物理学院）；Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and School of Electrical, Electronic and Mechanical Engineering, University of Bristol（布里斯托大学量子工程技术实验室、H.H.威尔斯物理实验室和电气、电子与机械工程学院）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔国立理工学院、内耳研究所）；University of Vienna, Faculty of Physics, Vienna Doctoral School in Physics, and Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院、维也纳物理博士学校和维也纳量子科学与技术中心（VCQ））；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所（IQOQI））；Sorbonne Université, CNRS, LIP6（索邦大学、法国国家科学研究中心、LIP6实验室）
We introduce a qubit-based version of the quantum switch, consisting in a variation of the Fermi problem. Two qubits start in a superposition state where one qubit is excited and the other in the ground state, but it is undefined which is the excited qubit. Then, after some time, if a photon is detected, we know that it must have experienced an emission by one atom and then an absorption and re-emission by the other one, but the ordering of the emission events by both qubits is undefined. While it is tempting to refer to this scenario as one with indefinite causality or a superposition of caus…
Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and no…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe distinctions/indistinctions, definiteness/indefiniteness, and distinguishability/indistinguishability. They throw some new light on the objective indefiniteness or literal interpretation of quantum mechanics (QM) advocated by Abner Shimony. This paper shows how the mathematics of QM is the math of indefiniteness and thus, literally and realistically interpret…
In this paper we propose a new ternary QRNG based on measuring located value indefinite observables with probabilities $1/4, 1/2,1/4$ and prove that every sequence generated is maximally unpredictable, 3-bi-immune (a stronger form of bi-immunity), and its prefixes are Borel normal. The ternary quantum random digits produced by the QRNG are algorithmically transformed into quantum random bits using an alphabetic morphism which preserves all the above properties.
Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a direct connection to the theory of multi-time quantum states. Specifically, we show that process matrices are equivalent to a particular class of pre- and post- selected quantum states. This offers a new conceptual point of view to the nature of process matrices. Our results also provide an explicit recipe to experimentally implement any process matrix in a pro…
We propose a thermodynamic refrigeration cycle which uses Indefinite Causal Orders to achieve non-classical cooling. The cycle cools a cold reservoir while consuming purity in a control qubit. We first show that the application to an input state of two identical thermalizing channels of temperature $T$ in an indefinite causal order can result in an output state with a temperature not equal to $T$. We investigate the properties of the refrigeration cycle and show that thermodynamically, the result is compatible with unitary quantum mechanics in the circuit model but could not be achieved classi…
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are probed in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super…
Quantum coherence is a prime resource in quantum computing and quantum communication. Quantum coherence of an arbitrary qubit state can be created at a remote location using maximally entangled state, local operation and classical communication. However, if there is a noisy channel acting on one side of the shared resource, then, it is not possible to create perfect quantum coherence remotely. Here, we present a method for the creation of quantum coherence at a remote location via the use of entangled state and indefinite causal order. We show this specifically for the superposition of two com…
By studying the set of correlations that are theoretically possible between physical systems without allowing for signalling of information backwards in time, we here identify correlations that can only be achieved if the time ordering between the systems is fundamentally indefinite. These correlations, if they exist in nature, must result from non-classical, non-deterministic time, and so may have relevance for quantum (or post-quantum) gravity, where a definite global time might not exist.
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 information bleaching refers to any physical process that removes quantum information from the initial state of the physical system. The no-hiding theorem proves that if information is lost from the initial system, then it cannot remain in the bipartite quantum correlation and must be found in the remainder of the Hilbert space. We show that when hiding map acts on the input state in the presence of indefinite causal order, then it is possible to hide quantum information in the correlation. One may ask, does it then violate the no-hiding theorem? We analyse this question and argue that in …
Is information causality a new physical principle? To answer this question, we first analytically derive the criteria of emergence of quantum correlations from information causality. Then it is shown that, as emergence criteria of quantum correlations, information causality and uselessness of coupler-based non-locality swapping can be regarded equivalent. Therefore, incapability of non-locality swapping using a coupler is as powerful as information causality in the single-out of quantum physics from generalized non-signalling models.
Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all causally ordered correlations. Using a generalized probabilistic framework, we propose three principles constraining bipartite correlations to the quantum bound. Our approach highlights the role of a measure of dependence other than mutual information for an information-theoretic reconstruction of causal structures in quantum theory.
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by introducing indefinite causal order ways of coin tossing and investigate this modern scenario. We find that an ideal-shape and fast-spreading uniform distribution can be prepared with our new model. First we will show how an always-symmetrical instantaneous distribution appears in an indefinite causal order quantum walk, which then paves the way for deriving con…
Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound from the axioms of nonlocality, relativistic causality and the existence of a classical limit. This derivation of Tsirelson's bound does not assume quantum mechanics yet suggests how Hilbert space is implicit in quantum correlations.
It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum state is given.
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…
Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three noisy channels for the case where the channels are in superposition of causal orders. We found that the quantum Fisher information increases as the number of causal orders increases for certain combinations. We also show that certain combinations of causal orders attain higher precision on bounds than others for the same number of causal orders. Based on our …
Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism of events. We propose a specific implementation of the scheme and recover the Quantum SWITCH, where quantum operations are performed in an order which is entangled with the state of a control qubit. Our scheme does not rely on any exotic quantum gravitational effect, but instead on phenomena which are naturally fuzzy in time, such as the decay of an excited…
I introduce environment - assisted invariance -- a symmetry related to causality that is exhibited by correlated quantum states -- and describe how it can be used to understand the nature of ignorance and, hence, the origin of probabilities in quantum physics.
In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures compatible with a model and quantifying the causal strengths are related but different questions. Recently much research have been directed towards the first question but considerably less attention is paid to the second one. In this paper we propose axioms for all reasonable quantitative measures of causality to obey. The axioms apply to a broad family of operati…
Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process a…
In the classical world, physical events always happen in a fixed causal order. However, it was recently revealed that quantum mechanics allows events to occur with indefinite causal order (ICO). In this study, we use an optical quantum switch to experimentally investigate the application of ICO in thermodynamic tasks. Specifically, we simulate the working system interacting with two identical thermal reservoirs in an ICO, observing the quantum heat extraction even though they are in thermal equilibrium where heat extraction is unaccessible by traditional thermal contact. Using such a process, …
Classical communication capacity of a channel can be enhanced either through a device called a 'quantum switch' or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the use of a quantum resource, but is it the same resource? Here this question is explored through simulating large sets of random channels. We find that quantum superposition always provides an advantage, while the quantum switch does not: it can either increase or decrease communication capacity. The origin of this discrepancy can be attributed to a subtle comb…
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: "superquantum" correlations, and nonlocal "jamming" of correlations. These models are consistent with some definitions of nonlocality and causality.
The quantum nonlocality is limited by relativistic causality, however, the reason is not fully understood yet. The relativistic causality condition on nonlocal correlations has been usually accepted as a prohibition of faster-than-light signaling, called no-signaling condition. We propose another causality condition from the observation that space-like separate events should have no causal relationship. It is proved that the new condition is stronger than no-signaling condition for a pair of binary devices. We derive the standard probability assignment rule, so-called Born rule, on quantum mea…
A quantum-controlled device may produce a scenario in which two general quantum operations can be performed in such a way that it is not possible to associate a definite order for the operations application. Such an indefinite causal order can be explored to produce nontrivial effects in quantum thermal devices. We investigate a measurement-powered thermal device that consists of generalized measurement channels with adjustable intensity parameters, where energy is exchanged with the apparatus in the form of work or heat. The measurement-based device can operate as a heat engine, a thermal acc…
We show that the non-locality together with the statistical character makes the world statistically separable. The super-luminal signal transmission is impossible. The quantum theory is therefore consistent with the relativity and the causality.
Recently, the principle of information causality has appeared as a good candidate for an information-theoretic principle that would single out quantum correlations among more general non-signalling models. Here we present results going in this direction; namely we show that part of the boundary of quantum correlations actually emerges from information causality.
