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Duality of quantum state verification and quantum data hiding

While they can be regarded as variants of quantum state discrimination, quantum state verification (QSV) and quantum data hiding (QDH) have so far been studied separately. QSV decides whether a given quantum state is close to the ideal state by performing available measurements M, with significantly lower sample complexity compared with direct application of quantum tomography. On the other hand, QDH is a cryptographic protocol that stores secret classical information in multipartite quantum states as security against multiple parties that can only perform measurements M. We show that a state requiring a large sample complexity for QSV exists if and only if a state that is useful for QDH exists. Moreover, we show that this relationship holds for any informationally complete measurement M. As an application, we show the existence of efficient QSV protocols and a limitation on QDH protocols using pure states by synthesizing research from both domains.

Sequential quantum maximum confidence discrimination

Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies including minimum-error and unambiguous state discrimination. We show that sequential state discrimination with equally high confidence can be realized only when positive-operator-valued measure elements for a maximum-confidence measurement are linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We establish a tradeoff between the disturbance of states and information gain in sequential state discrimination, namely, that the less a party learn in state discrimination in terms of a guessing probability, the more parties can participate in the sequential scenario. 

Factoring an integer with three oscillators and a qubit

A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating bits and allows for a device-independent development of algorithmic primitives. Here we advocate an alternative approach centered on the physical setup and show that sidestepping the standard approach can be leveraged to great benefit.
As an example, we consider hybrid qubit-oscillator systems with linear optics operations augmented by certain qubit-controlled Gaussian unitaries. The continuous variable Fourier transform and certain arithmetic operations have native realizations in such systems. We put this to algorithmic use and give a polynomial-time quantum factoring algorithm that uses only one qubit and three oscillators, independent of the number being factored.

Scaling up error mitigation of noisy measurements

In current quantum computers, measurement processes are inherently affected by noise. To address this unavoidable issue, a variety of techniques—collectively known as readout or measurement error mitigation—have been developed. These methods typically share a common foundation and face similar limitations: they rely on an accurate and complete characterization of measurement noise, followed by a strategy to correct its impact on the observed outcomes. Traditionally, these approaches have been applied to standard projective measurements and focus solely on errors occurring during the final readout stage. However, more advanced measurement schemes, such as those involving ancillary qubits and multi-qubit operations as part of the measurement protocol, demand more sophisticated tools—both at the tomographic and mitigation levels. Here, we propose a fully Bayesian measurement error mitigation pipeline: (I) We demonstrate how to perform Bayesian measurement tomography to accurately characterize noisy, informationally complete POVMs constructed using ancillary qubits and two-qubit gates; (II) we demonstrate how a Bayesian measurement error mitigation scheme effectively suppresses noise and ensures the physicality of the corrected outcomes by design, avoiding the emergence of unphysical results, and can be scaled up to problem sizes consistent with current QPUs qubit counts. Additionally, we show how the approach benefits from low-level access to detector data, offering improved performance and deeper insight into the measurement process.

Sound and efficient quantum system quizzing

The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. Existing certification techniques often fall short: they are either prohibitively expensive and rely on flawless state preparation and measurement (SPAM), or they fail to provide robust guarantees. While current SPAM-robust methods are complete, they lack soundness, meaning they do not ensure the correct implementation of quantum devices. In our recent work, we introduce quantum system quizzing, a simple yet sound certification protocol that enables the certification of entire quantum models in a black-box scenario under the dimension assumption. The protocol identifies deterministic input-output correlations of the ideal target model, which are tested during each round. This black box approach inherently eliminates SPAM errors. For single-qubit models, we derive rigorous sampling complexity guarantees. Most notably, we establish an inverse linear relationship between average gate infidelities and the number of successful protocol rounds, making the method highly practical for contemporary experimental setups. For multi-qubit quantum computers, we provide a sound certification proof in the infinite statistics regime and discuss the methods to derive sample complexity results in the finite statistics regime.

Information Causality and Communication Complexity

In a distributed computing scenario, two parties, Alice and Bob, aim to compute a given function with as little communication as possible. The communication cost, or complexity, depends not only on the function itself but also on the shared resources accessible to both parties, such as public randomness or entangled Bell pairs. This talk focuses on communication complexity in theories satisfying the information causality principle. The latter states that the information potentially available to Bob about Alice’s data cannot exceed the amount of information Alice sends to Bob. We generalize the information causality principle to any distributed computation scenario and prove that our new principle is stronger than the principle of non-trivial communication complexity in bounding the set of quantum correlations. First, we apply the new statement to several well-known functions, deriving one-way deterministic communication complexity bounds in a theory-independent manner. Next, we present a simple but elegant technique for obtaining polynomial inequalities from information causality, bounding the set of physical correlations in any Bell scenario. We derive new bounds on the set of quantum correlations, some of which exactly reproduce the boundary of the quantum set.

Storage and retrieval of two unitary channels

We address the fundamental task of converting n uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the n uses of the unknown unitary, and it produces the optimal state for discrimination between the two possible unitaries. Next, we show that incoherent "measure-and-prepare" retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary. We then identify the retrieval strategy that maximizes the probability of successfully and perfectly retrieving the unknown transformation. In the regime in which the fidelity between the two possible unitaries is large the probability of success scales as P_succ=1−O(n−2), which is a quadratic improvement with respect to the case in which the unitaries are drawn from the entire unitary group U(d) with uniform prior probability.  Finally, we present an optical experiment for this approach and assess the storage and retrieval quality using quantum tomography of states and processes. The results are discussed in relation to non-optimal measure-and-prepare strategy, highlighting the advantages of our protocol.