Faculty Profiles - BUSCEMI Francesco

PubMed

Macroscopicity and observational deficit in states, operations, and correlations* Open Access

Nagasawa, T; Wakakuwa, E; Kato, K; Buscemi, F

REPORTS ON PROGRESS IN PHYSICS Vol. 88 ( 11 ) 2025.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Reports on Progress in Physics Physical Society Great Britain

To understand the emergence of macroscopic irreversibility from microscopic reversible dynamics, the idea of coarse-graining plays a fundamental role. In this work, we develop a unified inferential framework formacroscopic states, that is, coarse descriptions of microscopic quantum systems that can be inferred from macroscopic measurements. Building on quantum statistical sufficiency and Bayesian retrodiction, we characterize macroscopic states through equivalent abstract (algebraic) and explicit (constructive) formulations. Central to our approach is the notion ofobservational deficit, which quantifies the degree of irretrodictability of a state relative to a prior and a measurement. This leads to a general definition of macroscopic entropy as an inferentially grounded measure of asymmetry under Bayesian inversion. We formalize this structure in terms ofinferential reference frames, defined by the pair consisting of a prior and a measurement, which encapsulate the observer's informational perspective. We then formulate a resource theory of microscopicity, treating macroscopic states as free states and introducing a hierarchy ofmacroscopicity-non-generating operations. This theory unifies and extends existing resource theories of coherence, athermality, and asymmetry. Finally, we apply the framework to study quantum correlations under observational constraints, introducing the notion ofobservational discordand deriving necessary and sufficient conditions for their vanishing in terms of information recoverability. This work is dedicated to Professor Ryszard Horodecki on the occasion of his 80th birthday, in deep admiration and gratitude for his pioneering contributions to quantum information theory.

DOI： 10.1088/1361-6633/ae140e

Port-based telecloning of an unknown quantum state

PubMed

Quantum Bayes' Rule and Petz Transpose Map from the Minimum Change Principle Open Access

Bai, G; Buscemi, F; Scarani, V

PHYSICAL REVIEW LETTERS Vol. 135 ( 9 ) page： 090203 2025.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Physical Review Letters

Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimum change principle and use it to derive a quantum Bayes' rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case, where Bayes' rule is obtained by minimizing several distances between the joint input-output distributions. When the change maximizes the fidelity, the quantum minimum change principle has a unique solution, and the resulting quantum Bayes' rule recovers the Petz transpose map in many cases.

DOI： 10.1103/5n4p-bxhm

Okada, R; Kato, K; Buscemi, F

PHYSICAL REVIEW A Vol. 111 ( 5 ) 2025.5

Publisher：Physical Review A

Telecloning is a protocol introduced by Murao et al. [Phys. Rev. A 59, 156 (1999)1050-294710.1103/PhysRevA.59.156] to distribute copies of an unknown quantum state to many receivers in a way that beats the trivial "clone-and-teleport"protocol. In the last decade, a new type of teleportation called port-based teleportation, in which the receiver can recover the state simply by looking at the correct port without having to actively perform correction operations, has been widely studied. In this paper, we consider the analog of telecloning, in which conventional teleportation is replaced by the port-based variant. To achieve this, we generalize the optimal measurement used in port-based teleportation and develop a new one that achieves port-based telecloning. Numerical results show that, in certain cases, the proposed protocol is strictly better than the trivial clone-and-teleport approach.

DOI： 10.1103/PhysRevA.111.052408

Causal and Noncausal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes Open Access

Buscemi, F; Gangwar, R; Goswami, K; Badhani, H; Pandit, T; Mohan, B; Das, S; Bera, MN

PRX QUANTUM Vol. 6 ( 2 ) 2025.4

Publisher：Prx Quantum

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of "revivals" and "backflows,"i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.

DOI： 10.1103/PRXQuantum.6.020316

Universal validity of the second law of information thermodynamics

Minagawa, S; Mohammady, MH; Sakai, K; Kato, K; Buscemi, F

NPJ QUANTUM INFORMATION Vol. 11 ( 1 ) 2025.2

Publisher：npj Quantum Information

Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell’s Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell’s Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon’s memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon’s memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal: it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.

DOI： 10.1038/s41534-024-00922-w

Generic increase of observational entropy in isolated systems

Nagasawa, T; Kato, K; Wakakuwa, E; Buscemi, F

PHYSICAL REVIEW RESEARCH Vol. 6 ( 4 ) 2024.12

Publisher：Physical Review Research

Observational entropy - a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy - was recently argued to play a key role in a modern formulation of statistical mechanics. Here, relying on algebraic techniques taken from Petz's theory of statistical sufficiency and on a Lévy-type concentration bound, we prove rigorous theorems showing how the observational entropy of a system undergoing a unitary evolution chosen at random tends to increase with overwhelming probability and to reach its maximum very quickly. More precisely, we show that for any observation that is sufficiently coarse with respect to the size of the system, regardless of the initial state of the system (be it pure or mixed), random evolution renders its state practically indistinguishable from the uniform (i.e., maximally mixed) distribution with a probability approaching 1 as the size of the system grows. The same conclusion holds not only for random evolutions sampled according to the unitarily invariant Haar distribution but also for approximate 2-designs, which are thought to provide a more physically and computationally reasonable model of random evolutions.

DOI： 10.1103/PhysRevResearch.6.043327

Tight conic approximation of testing regions for quantum statistical models and measurements Reviewed

M. Dall'Arno, F. Buscemi

Physics Letters A Vol. 526 2024.11

Observational entropy with general quantum priors

Bai, G; Safránek, D; Schindler, J; Buscemi, F; Scarani, V

QUANTUM Vol. 8 2024.11

The signaling dimension in generalized probabilistic theories Reviewed

Michele Dall'Arno, Alessandro Tosini, Francesco Buscemi

Quantum Information & Computation Vol. 24 ( 5-6 ) page： 411 - 424 2024.4

Publishing type：Research paper (scientific journal) Publisher：Rinton Press

The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. Thus, unlike other dimension measures - such as the dimension of the linear space or the maximum number of (jointly or pairwise) perfectly discriminable states - which examine the correlation space only along a single direction, the signaling dimension does not depend on the arbitrary choice of a specific operational task. In this sense, the signaling dimension summarizes the structure of the entire set of input/output correlations consistent with a given system in a single scalar quantity. For quantum theory, it was recently proved by Frenkel and Weiner in a seminal result that the signaling dimension coincides with the Hilbert space dimension. Here, we derive analytical and algorithmic techniques to compute the signaling dimension for any given system of any given generalized probabilistic theory. We prove that it suffices to consider extremal measurements with ray-extremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension. For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects as the problem of deriving the vertex description of a polytope given its face description, which can be conveniently solved by standard techniques such as the double description algorithm. For each such measurement, we recast the computation of the signaling dimension as a linear program, and we propose a combinatorial branch and bound algorithm to reduce its size. We apply our results to derive the extremal measurements with ray-extremal effects of a composition of two square bits (or squits) and prove that their signaling dimension is five, even though each squit has a signaling dimension equal to two.

DOI： 10.26421/QIC24.5-6-2

researchmap

Virtual Quantum Broadcasting Reviewed

Parzygnat, AJ; Fullwood, J; Buscemi, F; Chiribella, G

PHYSICAL REVIEW LETTERS Vol. 132 ( 11 ) page： 110203 2024.3

Authorship：Corresponding author Language：English Publisher：Physical Review Letters

The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show that, although quantum broadcasting cannot be achieved by any physical process, it can be achieved by a virtual process, described by a Hermitian-preserving trace-preserving map. This virtual process is canonical: it is the only map that broadcasts all quantum states, is covariant under unitary evolution, is invariant under permutations of the copies, and reduces to the classical broadcasting map when subjected to decoherence. We show that the optimal physical approximation to the canonical broadcasting map is the optimal universal quantum cloning, and we also show that virtual broadcasting can be achieved by a virtual measure-and-prepare protocol, where a virtual measurement is performed, and, depending on the outcomes, two copies of a virtual quantum state are generated. Finally, we use canonical virtual broadcasting to prove a uniqueness result for quantum states over time.

DOI： 10.1103/PhysRevLett.132.110203

PubMed

A complete and operational resource theory of measurement sharpness Reviewed

Buscemi, F; Kobayashi, K; Minagawa, S

Quantum Vol. 8 ( 1235 ) 2024.1

Maxwell's Demon Walks into Wall Street: Stochastic Thermodynamics Meets Expected Utility Theory Reviewed International coauthorship Open Access

Ducuara, AF; Skrzypczyk, P; Buscemi, F; Sidajaya, P; Scarani, V

PHYSICAL REVIEW LETTERS Vol. 131 ( 19 ) page： 197103 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Physical Review Letters

The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks's fluctuation relations, every α Rényi divergence between the forward process and its reverse has the operational meaning of the "certainty equivalent"of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=α-1. The two known cases α=1 and α=∞ are recovered and receive the new interpretation of being associated with a risk-neutral and an extreme risk-averse player, respectively. Among the new results, the condition for α=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences.

DOI： 10.1103/PhysRevLett.131.197103

Generalized resource theory of purity: one-shot purity distillation with local noisy operations and one way classical communication Reviewed International coauthorship

Chakraborty S., Nema A., Buscemi F.

IEEE International Symposium on Information Theory - Proceedings Vol. 2023-June page： 980 - 984 2023.8

Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication Reviewed International coauthorship

Buscemi F., Kobayashi K., Minagawa S., Perinotti P., Tosini A.

Quantum Vol. 7 ( 1035 ) 2023.7

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Quantum

While there is general consensus on the definition of incompatible POVMs, moving up to the level of instruments one finds a much less clear situation, with mathematically different and logically independent definitions of incompatibility. Here we close this gap by introducing the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility into one hierarchy of resource theories of communication between separated parties. The resource theories that we obtain are complete, in the sense that they contain complete families of free operations and monotones providing necessary and sufficient conditions for the existence of a transformation. Furthermore, our framework is fully operational, in the sense that free transformations are characterized explicitly, in terms of local operations aided by causally-constrained directed classical communication, and all monotones possess a game-theoretic interpretation making them experimentally measurable in principle. We are thus able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.

DOI： 10.22331/Q-2023-06-07-1035

Computing the quantum guesswork: a quadratic assignment problem Reviewed

Quantum Information and Computation Vol. 23 ( 9-10 ) page： 721 - 732 2023.7

Axioms for retrodiction: achieving time-reversal symmetry with a prior Reviewed

Parzygnat A.J., Buscemi F.

Quantum Vol. 7 ( 1013 ) 2023.5

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：Quantum

We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompass both classical and quantum theories alike. Classical Bayesian inversion and all rotated and averaged Petz recovery maps define retrodiction families in our sense. However, averaged rotated Petz recovery maps, including the universal recovery map of Junge–Renner–Sutter–Wilde–Winter, do not define retrodiction functors, since they fail to satisfy some compositionality properties. Among all the examples we found of retrodiction families, the original Petz recovery map is the only one that defines a retrodiction functor. In addition, retrodiction functors exhibit an inferential time-reversal symmetry consistent with the standard formulation of quantum theory. The existence of such a retrodiction functor seems to be in stark contrast to the many no-go results on time-reversal symmetry for quantum channels. One of the main reasons is because such works defined time-reversal symmetry on the category of quantum channels alone, whereas we define it on the category of quantum channels and quantum states. This fact further illustrates the importance of a prior in time-reversal symmetry.

DOI： 10.22331/Q-2023-05-23-1013

Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds Reviewed International coauthorship Open Access

Buscemi, F; Schindler, J; Safránek, D

NEW JOURNAL OF PHYSICS Vol. 25 ( 5 ) 2023.5

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：New Journal of Physics

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ‘coarse-grained’ state, which emerges from the measurement’s statistics by Bayesian retrodiction, without presuming any knowledge about the ‘true’ underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies.

DOI： 10.1088/1367-2630/accd11

Von Neumann's information engine without the spectral theorem Reviewed International journal Open Access

Minagawa Shintaro, Arai Hayato, Buscemi Francesco

PHYSICAL REVIEW RESEARCH Vol. 4 ( 3 ) 2022.8

Authorship：Last author Language：English Publisher：Physical Review Research

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational for the most part, von Neumann's argument departs from an operational narrative in its use of the spectral theorem. In this work, we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and, using these, we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold-Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.

DOI： 10.1103/PhysRevResearch.4.033091

Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off Reviewed International coauthorship International journal Open Access

Danageozian Arshag, Wilde Mark M., Buscemi Francesco

PRX QUANTUM Vol. 3 ( 2 ) 2022.4

Authorship：Last author Language：English Publisher：PRX Quantum

Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is commonly used in quantum computing when thermal noise is present. Interestingly, thermal noise has also been known to play a central role in quantum thermodynamics (QTD). This fact hints at the applicability of certain QTD statements in the QEC of thermal noise, which has been discussed previously in the context of Maxwell's demon. In this paper, we view QEC as a quantum heat engine with a feedback controller (i.e., a demon). We derive an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain, thereby also providing the latter with a physical meaning when it is negative. Further, we derive the second law of thermodynamics in the context of this QEC engine, operating with general quantum measurements. Finally, we show that, under a set of physically motivated assumptions, this leads to a fundamental triple-trade-off relation, which implies a trade-off between the maximum achievable fidelity of QEC and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess. A similar trade-off relation occurs for the thermodynamic efficiency of the QEC engine and the efficacy of the quantum measurement used for error identification.

DOI： 10.1103/PRXQuantum.3.020318

Guesswork of a quantum ensemble Open Access

Dall'Arno M., Buscemi F., Koshiba T.

IEEE Transactions on Information Theory 2022.1

Language：English Publisher：IEEE Transactions on Information Theory

The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.

DOI： 10.1109/TIT.2022.3146463