arXiv subjects

Carlo Maria Scandolo

Publications and source records attributed to Carlo Maria Scandolo.

At least 19 recordsLinked to original sources

arXiv2026

Towards the simulation of higher-order quantum resources: a general type-theoretic approach

Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are transformed by linear maps (superchannels) in order to simulate other gates. To develop a full hierarchy of quantum resources, beyond those first two orders, and to account for the fact that quantum protocols can interconvert resources of different orders, we need a theoretical framework that addresses all orders in a uniform manner. We introduce a framework based on a system of types, which label the different kinds of objects that are present at different orders. We equip the framework with a parallel product operation that modifies and generalizes the tensor product so as to be operationally meaningful for maps of distinct and arbitrary orders. Finally, we introduce a family of convex cones that generalize the notion of complete positivity to all orders, with the aim of characterizing the objects that are physically admissible, facilitating an operational treatment of quantum objects at any order.

quant-ph↗

arXiv2025

Choi-Defined Resource Theories

Many resource theories share an interesting property: An operation is free if and only if its renormalized Choi matrix is a free state. In this article, we refer to resource theories exhibiting this property as Choi-defined resource theories. We demonstrate how and under what conditions one can construct a Choi-defined resource theory, and we prove that when such a construction is possible, the free operations are all and only the completely resource-non-generating operations. Moreover, we examine resource measures, a complete family of monotones, and conversion distances in such resource theories.

quant-ph↗

arXiv2024

Bell Nonlocality in Classical Systems Coexisting with other System Types

The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can in principle be revealed by measurements. Here we show that this interpretation can in principle be falsified if classical systems coexist with other types of physical systems. To make this point, we construct a toy theory that (i) includes classical theory as a subtheory and (ii) allows classical systems to be entangled with another type of systems, called anti-classical. We show that our toy theory allows for the violation of Bell inequalities in two-party scenarios where one of the settings corresponds to a local measurement performed on a classical system alone. Building on this fact, we show that measurements outcomes in classical theory cannot, in general, be regarded as pre-determined by the state of an underlying reality.

quant-ph↗

arXiv2023

Constructor Theory as Process Theory

Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories of physics in terms of the (im)possibility to implement certain abstract "tasks" by means of physical processes. Process theory, on the other hand, pursues analogous characterisation goals in terms of the compositional structure of said processes, concretely presented through the lens of (symmetric monoidal) category theory. In this work, we show how to formulate fundamental notions of constructor theory within the canvas of process theory. Specifically, we exploit the functorial interplay between the symmetric monoidal structure of the category of sets and relations, where the abstract tasks live, and that of symmetric monoidal categories from physics, where concrete processes can be found to implement said tasks. Through this, we answer the question of how constructor theory relates to the broader body of process-theoretic literature, and provide the impetus for future collaborative work between the fields.

math.CT↗

arXiv2023

Thermodynamic state convertibility is determined by qubit cooling and heating

Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. At the core of this theory is the interconversion between athermality states, i.e., states out of thermal equilibrium. Here, we solve the question how athermality can be used to heat and cool other quantum systems that are initially at thermal equilibrium. We then show that the convertibility between quasi-classical resources (resources that do not exhibit coherence between different energy eigenstates) is fully characterized by their ability to cool and heat qubits, i.e., by two of the most fundamental thermodynamical tasks on the simplest quantum systems.

quant-ph↗

arXiv2023

Extending Resource Monotones using Kan Extensions

In this paper we generalize the framework proposed by Gour and Tomamichel regarding extensions of monotones for resource theories. A monotone for a resource theory assigns a real number to each resource in the theory signifying the utility or the value of the resource. Gour and Tomamichel studied the problem of extending monotones using set-theoretical framework when a resource theory embeds fully and faithfully into the larger theory. One can generalize the problem of computing monotone extensions to scenarios when there exists a functorial transformation of one resource theory to another instead of just a full and faithful inclusion. In this article, we show that (point-wise) Kan extensions provide a precise categorical framework to describe and compute such extensions of monotones. To set up monotone extensions using Kan extensions, we introduce partitioned categories (pCat)as a framework for resource theories and pCat functors to formalize relationship between resource theories. We describe monotones as pCat functors into the preorder of non-negative real numbers, and describe extending monotones along any pCat functor using Kan extensions. We show how our framework works by applying it to extend entanglement monotones for bipartite pure states to bipartite mixed states, to extend classical divergences to the quantum setting, and to extend a non-uniformity monotone from classical probabilistic theory to quantum theory.

quant-ph↗

arXiv2023

Quantum hypothesis testing between qubit states with parity

Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on the asymmetric setting of QHT, where the two types of decision errors are treated unequally, considering the operational limitations arising from the lack of a reference frame for chirality. This reference frame is associated with the group $\bbZ_2$ consisting of the identity transformation and the parity transformation. Thus, we have to discriminate between two qubit states by performing the $\bbZ_2$-invariant POVMs only. We start from the discrimination between two pure states. By solving the specific optimization problem we completely characterize the asymptotic behavior of the minimal probability of type-II error which occurs when the null hypothesis is accepted when it is false. Our results reveal that the minimal probability reduces to zero in a finite number of copies, if the $\bbZ_2$-twirlings of such two pure states are different. We further derive the critical number of copies such that the minimal probability reduces to zero. Finally, we replace one of the two pure states with a maximally mixed state, and similarly characterize the asymptotic behavior of the minimal probability of type-II error.

quant-ph↗

arXiv2023

Reply to the Comment on `The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'

This document is our reply to the Comment (Miloslav Znojil 2023 J. Phys. A: Math. Theor. 56, 038001) on our recent work titled `The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'. The original Comment consists of three addenda to our work. The first addendum claims that our work is ill-motivated as the motivating question, namely whether PT-symmetric quantum theory extends the standard quantum theory, was already answered in the literature. The second addendum points to some missing references in our work, and the third addendum suggests what constraints could lead to an extension of standard quantum theory. In our reply, we explain that the claim in the first addendum is a result of a misinterpretation of our motivating question. When interpreted correctly, the third addendum in the Comment in itself elaborates on why our motivating question is interesting and relevant. We also briefly comment on the prospects of an extension of standard quantum theory along the lines suggested in the third addendum. As our response to the second addendum, we explain our rationale behind citing certain references while leaving out others.

quant-ph↗

arXiv2023

Covariant influences for finite discrete dynamical systems

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be stated as follows: if we evolve the dynamical system for $n$ time steps and then we disturb it, it is the same as first disturbing the system with the same influence and then letting the system evolve for $n$ time steps. Applying the powerful machinery of resource theories, we develop a theory of covariant influences both when there is a purely deterministic evolution and when randomness is involved. Subsequently, we provide necessary and sufficient conditions for the transition between states under deterministic covariant influences and necessary conditions in the presence of stochastic covariant influences, predicting which transitions between states are forbidden. Our approach, for the first time, employs the framework of resource theories, borrowed from quantum information theory, to the study of finite discrete dynamical systems. The laws we articulate unify the behavior of different types of finite discrete dynamical systems, and their mathematical flavor makes them rigorous and checkable.

math-ph↗

arXiv2023

Resource Theory of Imaginarity: New Distributed Scenarios

The resource theory of imaginarity studies the operational value of imaginary parts in quantum states, operations, and measurements. Here we introduce and study the distillation and conversion of imaginarity in distributed scenario. This arises naturally in bipartite systems where both parties work together to generate the maximum possible imaginarity on one of the subsystems. We give exact solutions to this problem for general qubit states and pure states of arbitrary dimension. We present a scenario that demonstrates the operational advantage of imaginarity: the discrimination of quantum channels without the aid of an ancillary system. We then link this scenario to LOCC discrimination of bipartite states. We experimentally demonstrate the relevant assisted distillation protocol, and show the usefulness of imaginarity in the aforementioned two tasks.

quant-ph↗

arXiv2022

The operational foundations of PT-symmetric and quasi-Hermitian quantum theory

PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states, transformations, measurements and composition, which is a requirement for any physical theory. We aim to answer the question of whether a consistent physical theory with PT-symmetric observables extends standard quantum theory. We answer this question within the framework of general probabilistic theories, which is the most general framework for physical theories. We construct the set of states of a system that result from imposing PT-symmetry on the set of observables, and show that the resulting theory allows only one trivial state. We next consider the constraint of quasi-Hermiticity on observables, which guarantees the unitarity of evolution under a Hamiltonian with unbroken PT-symmetry. We show that such a system is equivalent to a standard quantum system. Finally, we show that if all observables are quasi-Hermitian as well as PT-symmetric, then the system is equivalent to a real quantum system. Thus our results show that neither PT-symmetry nor quasi-Hermiticity constraints are sufficient to extend standard quantum theory consistently.

quant-ph↗

arXiv2021

Universal structure of objective states in all fundamental causal theories

A crucial question is how objective and classical behavior arises from a fundamental physical theory. Here we provide a natural definition of a decoherence process valid in all causal theories, and show how its behavior can be extremely different from the quantum one. Remarkably, despite this, we prove that the so-called spectrum broadcast structure characterizes all objective states in every fundamental causal theory, exactly as in quantum mechanics. Our results show a stark contrast between the extraordinarily diverse decoherence behavior and the universal features of objectivity.

quant-ph↗

arXiv2021

Entanglement of a bipartite channel

The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, we rigorously study the entanglement of bipartite channels as a resource theory of quantum processes. We present an infinite and complete family of measures of dynamical entanglement, which gives necessary and sufficient conditions for convertibility under local operations and classical communication. Then we focus on the dynamical resource theory where free operations are positive partial transpose (PPT) superchannels, but we do not assume that they are realized by PPT pre- and post-processing. This leads to a greater mathematical simplicity that allows us to express all resource protocols and the relevant resource measures in terms of semi-definite programs. Along the way, we generalize the negativity from states to channels, and introduce the max-logarithmic negativity, which has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we use the non-positive partial transpose (NPT) resource theory to derive a no-go result: it is impossible to distill entanglement out of bipartite PPT channels under any sets of free superchannels that can be used in entanglement theory. This allows us to generalize one of the long-standing open problems in quantum information - the NPT bound entanglement problem - from bipartite states to bipartite channels. It further leads us to the discovery of bound entangled POVMs.

quant-ph↗

arXiv2021

Reconstructing quantum theory from diagrammatic postulates

We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbone of quantum theory concerns the manner in which systems and processes compose. Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. Therefore we first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the `fully quantum' systems as the final step. We propose two novel alternative manners of doing so, `no-leaking' (roughly that information gain causes disturbance) and `purity of cups' (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups & caps. Additionally, we show how the standard purification postulate can be seen as an immediate consequence of the symmetric purification postulate and purity of cups. Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a. CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can be subsumed under process theories. Secondly, we argue that the `sharp dagger' is indeed the right choice of a dagger structure as this sharpness is vital to the reconstruction.

quant-ph↗

arXiv2021

Resource theory of imaginarity: Quantification and state conversion

Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. In this work we develop theoretical methods for the resource theory of imaginarity, motivated by recent progress within theories of entanglement and coherence. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Moreover, we analyze the complexity of real and general operations in optical experiments, focusing on the number of unfixed wave plates for their implementation. We also discuss the role of imaginarity for local state discrimination, proving that any pair of real orthogonal pure states can be discriminated via local real operations and classical communication. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.

quant-ph↗

arXiv2021

Operational Resource Theory of Imaginarity

Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are actually essential, or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem both theoretically and experimentally, using the powerful tools of quantum resource theories. We show that - under reasonable assumptions - quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions which include the state-conversion problem for all qubit states and all pure states of any dimension, and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role for state discrimination: there exist real quantum states which can be perfectly distinguished via local operations and classical communication, but which cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. We confirm this phenomenon experimentally with linear optics, performing discrimination of different two-photon quantum states by local projective measurements. These results prove that complex numbers are an indispensable part of quantum mechanics.

quant-ph↗

arXiv2020

Dynamical Resources

Quantum channels are quintessential to quantum information, being used in all protocols, and describing how systems evolve in space and time. As such, they play a key role in the manipulation of quantum resources, and they are often resources themselves, called dynamical resources. This forces us to go beyond standard resource theories of quantum states. Here we provide a rigorous foundation for dynamical resource theories, where the resources into play are quantum channels, explaining how to manipulate dynamical resources with free superchannels. In particular, when the set of free superchannels is convex, we present a novel construction of an infinite and complete family of convex resource monotones, giving necessary and sufficient conditions for convertibility under free superchannels. After showing that the conversion problem in convex dynamical resource theories can be solved with conic linear programming, we define various resource-theoretic protocols for dynamical resources. These results serve as the framework for the study of concrete examples of theories of dynamical resources, such as dynamical entanglement theory.

quant-ph↗

arXiv2020

Dynamical Entanglement

Unlike the entanglement of quantum states, very little is known about the entanglement of bipartite channels, called dynamical entanglement. Here we work with the partial transpose of a superchannel, and use it to define computable measures of dynamical entanglement, such as the negativity. We show that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost. We discover a family of dynamical entanglement measures that provide necessary and sufficient conditions for bipartite channel simulation under local operations and classical communication and under operations with positive partial transpose.

quant-ph↗