arXiv subjects

Fabio Costa

Publications and source records attributed to Fabio Costa.

At least 37 records · Page 2Linked to original sources

arXiv2022

Indefinite temporal order without gravity

According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Recent research has shown that, combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order, which can be tested through the violation of Bell-type inequalities. According to Einstein, we shall assume physical equivalence of a uniform gravitational field and a corresponding acceleration of a reference system. Here we construct a non-gravitational scenario where accelerating particles interacting with optical cavities result in a violation of the temporal Bell inequalities analogous to the gravitational case. However, we find that the inequalities can also be violated by time-like events, exposing an ambiguity in their use as a theory-independent test of indefinite temporal order.

quant-ph↗

arXiv2022

A no-go theorem for superpositions of causal orders

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 processes: a pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process, namely it results in non-normalised probabilities when probed with certain operations. The result imposes constraints on novel resources for quantum information processing and on possible processes in a theory of quantum gravity.

quant-ph↗

arXiv2021

Effect of environment on the interferometry of clocks

Quantum interference of "clocks", namely of particles with time-evolving internal degrees of freedom (DOFs), is a promising avenue to test genuine general relativistic effects in quantum systems. The clock acquires which path information while experiencing different proper times on traversing the arms of the interferometer, leading to a drop in its path visibility. We consider scenarios where the clock is subject to environmental noise as it transits through the interferometer. In particular, we develop a generalized formulation of interferometric visibility affected by noise on the clock. We find that, for small noise and small proper time difference between the arms, the noise further reduces the visibility, while in more general situations it can either increase or reduce the visibility. As an example, we investigate the effect of a thermal environment constituted by a single field mode and show that the visibility drops further as the temperature is increased. Additionally, by considering noise models based on standard quantum channels, we show that interferometric visibility can increase or decrease depending on the type of noise and also the time scale and transition probabilities. The quantification of the effect of noise on the visibility -- particularly in the case of a thermal environment paves the way for a better estimate on the expected outcome in an actual experiment.

quant-ph↗

arXiv2021

Time-travelling billiard-ball clocks: a quantum model

General relativity predicts the existence of closed timelike curves (CTCs), along which an object could travel to its own past. A consequence of CTCs is the failure of determinism, even for classical systems: one initial condition can result in multiple evolutions. Here we introduce a new quantum formulation of a classic example, where a billiard ball can travel along two possible trajectories: one unperturbed and one, along a CTC, where it collides with its past self. Our model includes a vacuum state, allowing the ball to be present or absent on each trajectory, and a clock, which provides an operational way to distinguish the trajectories. We apply the two foremost quantum theories of CTCs to our model: Deutsch's model (D-CTCs) and postselected teleportation (P-CTCs). We find that D-CTCs reproduce the classical solution multiplicity in the form of a mixed state, while P-CTCs predict an equal superposition of the two trajectories, supporting a conjecture by Friedman et al. [Phys. Rev. D 42, 1915 (1990)].

quant-ph↗

arXiv2021

Witnessing quantum memory in non-Markovian processes

We present a method to detect quantum memory in a non-Markovian process. We call a process Markovian when the environment does not provide a memory that retains correlations across different system-environment interactions. We define two types of non-Markovian processes, depending on the required memory being classical or quantum. We formalise this distinction using the process matrix formalism, through which a process is represented as a multipartite state. Within this formalism, a test for entanglement in a state can be mapped to a test for quantum memory in the corresponding process. This allows us to apply separability criteria and entanglement witnesses to the detection of quantum memory. We demonstrate the method in a simple model where both system and environment are single interacting qubits and map the parameters that lead to quantum memory. As with entanglement witnesses, our method of witnessing quantum memory provides a versatile experimental tool for open quantum systems.

quant-ph↗

arXiv2021

Preprocessing operations and the reverse compression

The task of compression of data -- as stated by the source coding theorem -- is one of the cornerstones of information theory. Data compression usually exploits statistical redundancies in the data according to its prior distribution. Motivated by situations where one does not have access to the statistics of data, but has some information about a transformation that is going to be applied to it, we propose a novel method for data compression called reverse compression. It is defined in such a way that works for both classical and quantum information processes, and furthermore relies exclusively on the channel to be used: all input data leading to indistinguishable outputs is compressed to the same state, regardless of their prior distribution. Moreover, this process can be characterized as a higher order operation within the type of preprocessing. We also consider as an example the application of the method to the classical and quantum erasure channel. The examples suggest that noiseless reverse compression can take place only in trivial cases, although meaningful instances of noisy reverse compression can exist.

quant-ph↗

arXiv2020

Classical communication through quantum causal structures

Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism, we formulate different classical capacities for a bi-partite quantum process. We find that a one-way communication protocol through an arbitrary process cannot outperform a causally separable process, i.e., we can send at most one bit per qubit. Next, we study bi-directional communication through a causally separable process. Our result shows, a bi-directional protocol cannot exceed the limit of one way communication protocol. Finally, we generalise this result to multi-party broadcast communication protocol through a definite ordered process.

quant-ph↗

arXiv2020

Bell's Theorem for Temporal Order

Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed time order while in general relativity temporal order is influenced by the distribution of matter. When the distribution of matter requires a quantum description, temporal order is expected to become non-classical -- a scenario beyond the scope of current theories. Here we provide a direct description of such a scenario. We consider a massive body in a spatial superposition and show how it leads to "entanglement" of temporal orders between time-like events in the resulting space-time. This entanglement enables accomplishing a task, violation of a Bell inequality, that is impossible under classical temporal order. Violation of the inequality means that temporal order becomes non-classical -- it cannot be described by locally defined classical variables. Our approach provides a quantitative method for investigating quantum aspects of space-time and gravity.

quant-ph↗

arXiv2020

Computational advantage from quantum-controlled ordering of gates

It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more general kind of quantum computing, that allows transformations on blackbox quantum gates that are impossible in a circuit with fixed order. Here we show that this model of quantum computing is physically realizable, by proposing an interferometric setup that can implement such a quantum control of the order between the gates. We show that this new resource provides a reduction in computational complexity: we propose a problem that can be solved using $O(n)$ blackbox queries, whereas the best known quantum algorithm with fixed order between the gates requires $O(n^2)$ queries. Furthermore, we conjecture that solving this problem in a classical computer takes exponential time, which may be of independent interest.

quant-ph↗

arXiv2019

Assisted Macroscopic Quantumness

It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce a variant of the Wigner's friend experiment in which a multiparticle quantum system is observed by the friend. The friend undergoes rapid decoherence through her interactions with the environment. In the usual version of this thought experiment, decoherence removes the need for Wigner to treat her as a quantum system. However, for our variant we prove theoretically and observe experimentally that there exist partitions of the subsystems in which the friend is entangled with one of the particles in assistance with the other particle, as observed by Wigner. Importantly, we show that the friend is indispensable for the entanglement to be observed. Hence Wigner is compelled to treat the friend as part of a larger quantum system. By analyzing our scenario in the context of a quantum key distribution protocol, we show that a semi-classical description of the experiment is suboptimal for security analysis, highlighting the significance of the quantum description of the friend.

quant-ph↗

arXiv2019

Reversible time travel with freedom of choice

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: Three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.

gr-qc↗

arXiv2019

Violation of a causal inequality in a spacetime with definite causal order

Processes with an indefinite causal structure may violate a causal inequality, which quantifies quantum correlations that arise from a lack of causal order. In this paper, we show that when the inequalities are analysed with a Gaussian-localised field theoretic definition of particles and labs, the causal indeterminacy of the fields themselves allows a causal inequality to be violated within the causal structure of Minkowski spacetime. We quantify the violation of the inequality and determine the optimal ordering of observers.

quant-ph↗

arXiv2019

Causal order as a resource for quantum communication

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal uncertainty in the causal order forbids asymptotic quantum communication, while still enabling the noisy transfer of classical information. Therefore causal order, like shared entanglement, is an additional resource for communication. The result is formulated within an asymptotic setting for processes with no fixed causal order, which sets a basis for a quantum information theory in general quantum causal structures.

quant-ph↗

arXiv2019

Quantum Markovianity as a supervised learning task

Supervised learning algorithms take as input a set of labelled examples and return as output a predictive model. Such models are used to estimate labels for future, previously unseen examples drawn from the same generating distribution. In this paper we investigate the possibility of using supervised learning to estimate the dimension of a non-Markovian quantum environment. Our approach uses an ensemble learning method, the Random Forest Regressor, applied to classically simulated data sets. Our results indicate this is a promising line of research.

quant-ph↗

arXiv2018

Relativity of quantum superpositions

In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical relevance. On the other hand, in quantum theory the scenario where one system, A, is localised around certain position while another system B is in a spatial superposition is considered to be physically different from the scenario where A is in a superposition, while B is localised. Different physical effects are anticipated in the two scenarios especially when the two systems have widely different masses. Here we show that for any superposed amplitudes that are related by a symmetry transformation, the above scenarios are physically equivalent: probabilities for any measurement are the same whether we assign the superposition state to system A or to system B. More generally, linearity of quantum theory guarantees that if a theory is invariant under some symmetry transformations it is necessarily also invariant under their arbitrary `superpositions'. Thus the notion of a superposition turns out to be relative to the choice of coordinates, once it is realised that relations between coordinates do not need to be classical.

quant-ph↗

arXiv2018

A Unifying Framework for Spatial and Temporal Quantum Correlations

Measurements on a single quantum system at different times reveal rich non-classical correlations similar to those observed in spatially separated multi-partite systems. Here we introduce a theory framework that unifies the description of temporal, spatial, and spatio-temporal resources for quantum correlations. We identify, and experimentally demonstrate simple cases where an exact mapping between the domains is possible. We then identify correlation resources in arbitrary situations, where not all spatial quantum states correspond to a process and not all temporal measurements have a spatial analogue. These results provide a starting point for the systematic exploration of multi-point temporal correlations as a powerful resource for quantum information processing.

quant-ph↗

arXiv2018

Causation does not explain contextuality

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

quant-ph↗

arXiv2018

A quantum causal discovery algorithm

Finding a causal model for a set of classical variables is now a well-established task---but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally-ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm provides a first step towards more general methods for quantum causal discovery.

quant-ph↗