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G. Chiribella

Publications and source records attributed to G. Chiribella.

At least 19 recordsLinked to original sources
arXiv2015

Universal super-replication of unitary gates

Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that $N$ parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on $O(\log N)$ qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.

quant-ph↗
arXiv2014

Conservation of information and the foundations of quantum mechanics

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.

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arXiv2014

Optimal asymptotic cloning machines

We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic fidelity enjoys a universality property, as its scaling does not depend on the specific details of the set of input states, but only on the number of parameters needed to specify them.

quant-ph↗
arXiv2014

Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks

It has been recently shown that probabilistic protocols based on postselection boost the performances of phase estimation and the replication of quantum clocks. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metrology can simulate cloning in the macroscopic limit for arbitrary sets of states, provided that the performance of the simulation is measured by testing small groups of clones.

quant-ph↗
arXiv2014

Measurement sharpness cuts nonlocality and contextuality in every physical theory

Gathering data through measurements is at the basis of every experimental science. Ideally, measurements should be repeatable and, when extracting only coarse-grained data, they should allow the experimenter to retrieve the finer details at a later time. However, in practice most measurements appear to be noisy. Here we postulate that, despite the imperfections observed in real life experiments, there exists a fundamental level where all measurements are ideal. Combined with the requirement that ideal measurements remain so when coarse-grained or applied in parallel on spacelike separated systems, our postulate places a powerful constraint on the amount of nonlocality and contextuality that can be found in an arbitrary physical theory, bringing down the violation of Bell and Kocher-Specker inequalities near to its quantum value. In addition, it provides a new compelling motivation for the principles of Local Orthogonality and Consistent Exclusivity, recently proposed for the characterization of the quantum set of probability distributions.

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arXiv2013

Optimal networks for Quantum Metrology: semidefinite programs and product rules

We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at each time step. We formulate the search of the optimal network as a semidefinite program and use duality theory to give an alternative expression for the maximum payoff achieved by estimation. Combining this formulation with a technique devised by Mittal and Szegedy we prove a general product rule for the joint estimation of independent processes, stating that the optimal joint estimation can achieved by estimating each process independently, whenever the figure of merit is of a product form. We illustrate the result in several examples and exhibit counterexamples showing that the optimal joint network may not be the product of the optimal individual networks if the processes are not independent or if the figure of merit is not of the product form. In particular, we show that entanglement can reduce by a factor K the variance in the estimation of the sum of K independent phase shifts.

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arXiv2013

Quantum computations without definite causal structure

We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical switch of black boxes, where two input black boxes are arranged in two different orders conditionally on the value of a classical bit. The quantum version of this transformation-the quantum switch-produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure. Simulating these transformations in a circuit with fixed causal structure requires either postselection, or an extra query to the input black boxes.

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arXiv2012

Normal completely positive maps on the space of quantum operations

Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quantum superinstruments, namely measures with values in the set of quantum supermaps, and derive a dilation theorem for them that is analogue to Ozawa's theorem for quantum instruments. The three dilation theorems presented here show that all the supermaps defined in this paper can be implemented by connecting devices in quantum circuits.

math-ph↗
arXiv2012

Perfect discrimination of no-signalling channels via quantum superposition of causal structures

A no-signalling channel transforming quantum systems in Alice's and Bob's laboratories is compatible with two different causal structures: (A < B) Alice's output causally precedes Bob's input and (B< A) Bob's output causally precedes Alice's input. I show that a quantum superposition of circuits operating within these two causal structures enables the perfect discrimination between no-signalling channels that can not be perfectly distinguished by any ordinary circuit.

quant-ph↗
arXiv2012

Quantum Theory, namely the pure and reversible theory of information

After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental physical theory cannot be described using the ordinary language of Physics? Here we offer a contribution to the problem from the angle of Quantum Information, providing a short non-technical presentation of a recent derivation of Quantum Theory from information-theoretic principles. The broad picture emerging from the principles is that Quantum Theory is the only standard theory of information compatible with the purity and reversibility of physical processes.

quant-ph↗
arXiv2012

Teleportation transfers only speakable quantum information

We show that a quantum clock cannot be teleported without prior synchronization between sender and receiver: every protocol using a finite amount of entanglement and an arbitrary number of rounds of classical communication will necessarily introduce an error in the teleported state of the clock. Nevertheless, we show that entanglement can be used to achieve synchronization with precision higher than any classical correlation allows, and we give the optimized strategy for this task. The same results hold also for arbitrary continuous quantum reference frames, which encode general unspeakable information,-information that cannot be encoded into a number, but instead requires a specific physical support, like a clock or a gyroscope, to be conveyed.

quant-ph↗
arXiv2011

Informational derivation of Quantum Theory

Quantum theory can be derived from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of information-processing that can be regarded as a standard. One postulate-purification-singles out quantum theory within this class. The main structures of quantum theory, such as the representation of mixed states as convex combinations of perfectly distinguishable pure states, are derived directly from the principles without using the Hilbert space framework.

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arXiv2011

Group theoretic structures in the estimation of an unknown unitary transformation

This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the optimal estimation strategy. The paper also contains a discussion about the role of entanglement between the representation and multiplicity spaces and about the optimality of square-root measurements.

quant-ph↗
arXiv2010

Probabilistic theories with purification

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows one to prove most of the basic features of quantum mechanics, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

quant-ph↗
arXiv2010

Optimal quantum learning of a unitary transformation

We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine), and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving. Differing from the case of quantum cloning, where the incoherent "measure-and-prepare" strategies are typically suboptimal, in the case of learning the "measure-and-rotate" strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the "measure-and-rotate" strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.

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arXiv2009

A short impossibility proof of Quantum Bit Commitment

Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment-bindingness tradeoff. A strengthened and explicit impossibility proof has been given in: G. M. D'Ariano, D. Kretschmann, D. Schlingemann, and R. F. Werner, Phys. Rev. A 76, 032328 (2007), in the Heisenberg picture and in a C*-algebraic framework, considering all conceivable protocols in which both classical and quantum information are exchanged. In the present paper we provide a new impossibility proof in the Schrodinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs, with each single-party strategy represented by a conditional comb. We prove that assuming a stronger notion of concealment--worst-case over the classical information histories--allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment-bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with respect to the comb-discriminability distance.

quant-ph↗
arXiv2009

Optimal cloning of unitary transformations

After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms the optimal measure-and-reprepare cloning strategy. Applications are outlined, including two-way quantum cryptographic protocols.

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