arXiv subjects

Jason L. Pereira

Publications and source records attributed to Jason L. Pereira.

12 recordsLinked to original sources

arXiv2026

A no-go theorem for privacy in distributed sensing using Gaussian states

In the discrete variable setting, entangled resource states allow a set of parties to learn a global function of a set of spatially separated systems, whilst keeping the local parameters of those systems completely private. In the continuous variable setting, distributed sensing has been carried out using Gaussian resource states, but without the same guarantees about privacy. Here, we show that perfect privacy is impossible to achieve for any distributed sensing protocol that uses Gaussian states as a resource. We also introduce a measure of relative privacy, bounding the degree to which any Gaussian distributed sensing protocol can keep local parameters hidden.

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arXiv2025

Out-of-distribution generalisation for learning quantum channels with low-energy coherent states

When experimentally learning the action of a continuous variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is using low energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low energy inputs but very differently for high energy inputs. They may also act similarly on coherent state inputs but differently on non-classical inputs. Extrapolating the behaviour of a channel for more general input states from its action on the far more limited set of low energy coherent states is a case of out-of-distribution generalisation. To be sure that such generalisation gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low energy coherent state inputs, one can bound how different the input-output relations are for any (high energy or highly non-classical) input. This proves out-of-distribution generalisation is always possible for learning quantum channels using low energy coherent states, as long as enough samples are used.

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arXiv2024

Learning to Classify Quantum Phases of Matter with a Few Measurements

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g., cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g., single qubit measurements, but unable to perform a universal set of gates.

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arXiv2023

Continuous variable port-based teleportation

Port-based teleportation is generalization of the standard teleportation protocol which does not require unitary operations by the receiver. This comes at the price of requiring $N>1$ entangled pairs, while $N=1$ for the standard teleportation protocol. The lack of correction unitaries allows port-based teleportation to be used as a fundamental theoretical tool to simulate arbitrary channels with a general resource, with applications to study fundamental limits of quantum communication, cryptography and sensing, and to define general programmable quantum computers. Here we introduce a general formulation of port-based teleportation in continuous variable systems and study in detail the $N=2$ case. In particular, we interpret the resulting channel as an energy truncation and analyse the kinds of channels that can be naturally simulated after this restriction.

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arXiv2023

Analytical bounds for non-asymptotic asymmetric state discrimination

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding the set of achievable errors, using the trace norm, the fidelity, and the quantum Chernoff bound. The upper bound is asymptotically tight and the lower bound is exact for pure states. Unlike asymptotic bounds, our bounds give error values instead of exponents, so can give more precise results when applied to finite-copy state discrimination problems.

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arXiv2023

Quantum-enhanced cluster detection in physical images

Identifying clusters in data is an important task in many fields. In this paper, we consider situations in which data live in a physical world, so we have to first collect the images using sensors before clustering them. Using sensors enhanced by quantum entanglement, we can image surfaces more accurately than using purely classical strategies. However, it is not immediately obvious if the advantage we gain is robust enough to survive data processing steps such as clustering. It has previously been found that using quantum-enhanced sensors for imaging and pattern recognition can give an advantage for supervised learning tasks, and here we demonstrate that this advantage also holds for an unsupervised learning task, namely clustering.

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arXiv2021

Symplectic decomposition from submatrix determinants

An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation. Whilst the diagonal form is easy to find, the process for finding the diagonalising symplectic can be more difficult, and a common, existing method requires taking matrix powers, which can be demanding analytically. Inspired by a recently presented technique for finding the eigenvectors of a Hermitian matrix from certain submatrix eigenvalues, we derive a similar method for finding the diagonalising symplectic from certain submatrix determinants, which could prove useful in Gaussian quantum information.

math-ph↗

arXiv2021

Bounding the benefit of adaptivity in quantum metrology using the relative fidelity

Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimising this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an $N$-use protocol is no more than $N^2$ times the one-shot QFI.

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arXiv2021

Idler-free channel position finding

Entanglement is a powerful tool for quantum sensing, and entangled states can greatly boost the discriminative power of protocols for quantum illumination, quantum metrology, or quantum reading. However, entangled state protocols generally require the retention of an idler state, to which the probes are entangled. Storing a quantum state is difficult and so technological limitations can make protocols requiring quantum memories impracticable. One alternative is idler-free protocols that utilise non-classical sources but do not require any idler states to be stored. Here we apply such a protocol to the task of channel position finding. This involves finding a target channel in a sequence of background channels, and has many applications, including quantum sensing, quantum spectroscopy, and quantum reading.

quant-ph↗

arXiv2021

Bounds on amplitude damping channel discrimination

Amplitude damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the performance of such protocols. Since adaptivity has been shown to improve the performance of discrimination protocols, bounds on the distinguishability of AD channels must take this into account. In this paper, we use both channel simulation and a bound based on the diamond norm to significantly tighten the upper bound on the trace norm between the possible outputs of binary channel discrimination protocols acting on AD channels (and hence the lower bound on the error probability of such protocols). The diamond norm between any two AD channels is found analytically, giving the optimal error probability for a one-shot discrimination protocol. We also present a tighter lower bound on the achievable trace norm between protocol outputs (and a corresponding upper bound on the achievable error probability). The upper and lower bounds are compared with existing bounds and then applied to quantum hacking and biological quantum sensing scenarios.

quant-ph↗

arXiv2021

Optimal environment localization

Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multi-mode system. We derive bounds for the ultimate error probability affecting this multi-ary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).

quant-ph↗

arXiv2019

Fundamental limits to quantum channel discrimination

What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation.

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