arXiv subjects

Juan Carlos Garcia-Escartin

Publications and source records attributed to Juan Carlos Garcia-Escartin.

At least 19 recordsLinked to original sources

arXiv2026

Lie algebraic invariants in quantum linear optics

Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare. Thus, a deeper understanding of linear optical state preparation is needed. In this work, we give a recipe to derive conserved quantities in the evolution of arbitrary states along any possible passive linear interferometer. One example of such an invariant is the spectrum of a density matrix mapped onto the Lie algebra of passive linear optical Hamiltonians. These invariants give necessary conditions for exact state preparation: if the input and output states have different invariants, it is impossible to design a passive linear interferometer that evolves one into the other. Moreover, we provide a lower bound to the distance between an output and target state based on the distance between their invariants. This gives a necessary condition for approximate or heralded state preparations. Therefore, the invariants allow us to narrow the search when trying to prepare useful entangled states, like NOON states, from easy-to-prepare states, like Fock states. We conclude that future exact and approximate state preparation methods will need to consider the necessary conditions given by our invariants to weed out impossible linear optical evolutions.

quant-ph↗

arXiv2025

Routing and wavelength assignment in quantum key distribution networks: power control heuristics for quantum-classical multiplexing

As quantum key distribution networks grow in size and complexity, resource assignment has become increasingly important. In passive optical networks without wavelength conversion, we need to assign a full route between origin and destination with the same wavelength from a finite set. This problem is computationally intensive and the common solution in classical optical networks is using heuristics. We adapt these heuristics to hybrid quantum networks where the quantum channel can share some of the optical links with classical channels. In this quantum-classical multiplexing, nonlinear effects can become the limiting factor in the range of the network. The signal in the classical channels can be subject to Raman Scattering or Four-Wave-Mixing and produce light in the quantum channels. While these processes are not efficient, even a single photon can ruin the quantum channel. We propose heuristics for the routing and wavelength assignment problem for hybrid quantum-classical networks with power control for the classical channels. By keeping the transmitted power to its bare functional minimum, we can reduce the interference to the quantum channels. We study their efficiency under different scenarios.

quant-ph↗

arXiv2025

Finding eigenvectors with a quantum variational algorithm

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis (QPCA) on unknown input mixed states. These algorithms can all be run with low depth quantum circuits, suitable for an efficient implementation on noisy intermediate state quantum computers (NISQC) and, with some restrictions, on linear optical systems. Limitations and potential applications are discussed.

quant-ph↗

arXiv2024

Routing and wavelength assignment in hybrid networks with classical and quantum signals

Quantum Key Distribution has become a mature quantum technology that has outgrown dedicated links and is ready to be incorporated into the classical infrastructure. In this scenario with multiple potential nodes, it is crucial having efficient ways to allocate the network resources between all the potential users. We propose a simple method for routing and wavelength assignment in wavelength multiplexed networks in which classical and quantum channels coexist. The proposed heuristics take into account the specific requirements of quantum key distribution and focus on keeping at bay the contamination of the quantum channels by photons coming from the classical signals by non-linear processes, among others. These heuristics reduce the shared path between classical and quantum channels and improve the signal-to-noise ratio in the quantum channels, improving their quantum key rate. We compare the results to the usual classical RWA approach.

quant-ph↗

arXiv2023

No-go theorems for photon state transformations in quantum linear optics

We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity that appears in all allowed optical transformations. We comment some examples and numerical applications, with example code, and give three general no-go results. These include (i) the impossibility of deterministic transformations which redistribute the photons from one to two different modes, (ii) a proof that it is impossible to generate a perfect Bell state in heralded schemes with a separable input for any number of ancillary photons and modes and a fixed herald and (iii) a restriction for the conversion between different types of entanglement (converting GHZ to W states).

quant-ph↗

arXiv2023

Multiple photon Hamiltonian in linear quantum optical networks

We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective Hamiltonian of the optical system for a single photon and comes from relating the evolution in the Lie group that describes the unitary evolution matrices in the Hilbert space of the photon states to the evolution in the Lie algebra of the Hamiltonians for one and multiple photons. We give a few examples of how a group theory approach can shed light on some properties of devices with two input ports.

quant-ph↗

arXiv2023

A method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe

The evolution of quantum light through linear optical devices can be described by the scattering matrix $S$ of the system. For linear optical systems with $m$ possible modes, the evolution of $n$ input photons is given by a unitary matrix $U=φ_{m,M}(S)$ given by a known homomorphism, $φ_{m,M}$, which depends on the size of the resulting Hilbert space of the possible photon states, $M$. We present a method to decide whether a given unitary evolution $U$ for $n$ photons in $m$ modes can be achieved with linear optics or not and the inverse transformation $φ_{m,M}^{-1}$ when the transformation can be implemented. Together with previous results, the method can be used to find a simple optical system which implements any quantum operation within the reach of linear optics. The results come from studying the adjoint map bewtween the Lie algebras corresponding to the Lie groups of the relevant unitary matrices.

quant-ph↗

arXiv2023

QOptCraft: A Python package for the design and study of linear optical quantum systems

The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when designing quantum experiments with linear interferometers. The methods include functions that compute the quantum evolution matrix for n photons from the classical description of the system and inverse methods that, for any desired quantum evolution, will either give the complete description of the experimental system that realizes that unitary evolution or, when this is impossible, the complete description of the linear system which approximates the desired unitary with a locally minimal error. The functions in the package include implementations of different known decompositions that translate the classical scattering matrix of a linear system into a list of beam splitters and phase shifters and methods to compute the effective Hamiltonian that describes the quantum evolution of states with n photons. The package is completed with routines for useful tasks like generating random linear optical systems and computing matrix logarithms. The routines are chosen to avoid usual numerical problems when dealing with the unitary matrices that appear in the description of linear systems.

quant-ph↗

arXiv2023

The SWITCH test for discriminating quantum evolutions

We propose a quantum circuit to discriminate between two arbitrary quantum evolution operators. It permits to test the equality of two quantum operators and to estimate a fidelity measure of them. The relation of the proposal to the SWAP test for discriminating two quantum states is analyzed. We also discuss potential applications for the discrimination of quantum communication channels and possible laboratory implementations with light along the same lines of recent experimental realizations of quantum superpositions of causal orders exploiting the different degrees of freedom of photons. We also discuss hardware efficient realizations for noisy intermediate scale quantum computers.

quant-ph↗

arXiv2021

A quantum algorithm for computing the Carmichael function

Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a probability as close to 1 as desired. The algorithm requires $O((\log n )^3n^3)$ quantum operations, or $O(\log\log n (\log n)^4 n^2)$ operations using fast multiplication. Verification, quantum optimizations and applications to RSA and primality tests are also discussed.

quant-ph↗

arXiv2021

Quantum collision finding for homomorphic hash functions

Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $\oplus$-linear hash functions and for certain multiplicative homomorphic hash schemes.

cs.CR↗

arXiv2020

Optimal approximation to unitary quantum operators with linear optics

Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov's theorem from differential geometry, we propose an iterative method that, for any arbitrary quantum operator $U$ acting on $n$ photons in $m$ modes, returns an operator $\widetilde{U}$ which can be implemented with linear optics. The approximation method is locally optimal and converges. The resulting operator $\widetilde{U}$ can be translated into an experimental optical setup using previous results.

quant-ph↗

arXiv2020

Detector blinding attacks on counterfactual quantum key distribution

Counterfactual quantum key distribution protocols allow two sides to establish a common secret key using an insecure channel and authenticated public communication. As opposed to many other quantum key distribution protocols, part of the quantum state used to establish each bit never leaves the transmitting side, which hinders some attacks. We show how to adapt detector blinding attacks to this setting. In blinding attacks, gated avalanche photodiode detectors are disabled or forced to activate using bright light pulses. We present two attacks that use this ability to compromise the security of counterfactual quantum key distribution. The first is a general attack but technologically demanding (the attacker must be able to reduce the channel loss by half). The second attack could be deployed with easily accessible technology and works for implementations where single photon sources are approximated by attenuated coherent states. The attack is a combination of a photon number splitting attack and the first blinding attack which could be deployed with easily accessible technology. The proposed attacks show counterfactual quantum key distribution is vulnerable to detector blinding and that experimental implementations should include explicit countermeasures against it.

quant-ph↗

arXiv2020

Attacking quantum key distribution by light injection via ventilation openings

Quantum cryptography promises security based on the laws of physics with proofs of security against attackers of unlimited computational power. However, deviations from the original assumptions allow quantum hackers to compromise the system. We present a side channel attack that takes advantage of ventilation holes in optical devices to inject additional photons that can leak information about the secret key. We experimentally demonstrate light injection on an ID~Quantique Clavis2 quantum key distribution platform and show that this may help an attacker to learn information about the secret key. We then apply the same technique to a prototype quantum random number generator and show that its output is biased by injected light. This shows that light injection is a potential security risk that should be addressed during the design of quantum information processing devices.

quant-ph↗

arXiv2019

Physical Unclonable Functions with Boson Sampling

Boson sampling is a problem for which quantum devices could prove to go beyond classical computing using only linear optics and photon preparation and counting. While theoretically important, there is a lack of practical applications for this task. This paper presents a way to turn any boson sampling device for which there are certain fabrication limits into a physically unclonable function which could be used in identification systems and other security protocols. For a minimum fabrication error, there are scenarios for which the photon distribution at the output of two different devices has a minimum distance and they can be told apart. When compared to classical PUFs these linear optical tokens have the advantage that, for the right choice of parameters, there is a computational guarantee that no classical computer can simulate the output. The paper describes the basic limitations of boson sampling which allow these results and gives a possible choice for a challenge-response identification protocol. This gives a direct application of boson sampling which could be simpler than solving the general problem.

quant-ph↗

arXiv2017

Robustness of QMA against witness noise

Using the tool of concatenated stabilizer coding, we prove that the complexity class QMA remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying protocols but also attacking the relationship between the complexity classes QMA, QCMA and BQP, which can be reformulated in this unified framework of a verifying protocol receiving a disturbed witness. While QCMA and BQP are described by fully dephasing and depolarizing channels on the witness qubits, respectively, our result proves QMA to be robust against 27% dephasing and 18% depolarizing noise.

quant-ph↗

arXiv2017

Hidden probe attacks on ultralong fiber laser key distribution systems

In ultralong fiber laser key distribution, two sides use standard optical equipment to create kilometer long fiber lasers in a communication link to establish a secret key. Its security rests on the assumption that any attacker would need much more sophisticated equipment and techniques than those of the legitimate user in order to discover the generated key. We present a challenge to that assumption with a hidden probe attack in which the eavesdropper hides a weak signal in the unavoidable noise floor that appears in the laser during amplification and probes with it the configuration of one or both communication parties. We comment how this attack can compromise different proposals for ultralong laser key distribution and propose possible countermeasures.

physics.app-ph↗

arXiv2017

Quantum arithmetic with the Quantum Fourier Transform

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

quant-ph↗