arXiv subjects

Dave Touchette

Publications and source records attributed to Dave Touchette.

At least 19 recordsLinked to original sources

arXiv2026

Asymptotic Compression of Interactive Quantum Communication using Type-Constrained de Finetti Reduction

For many information processing tasks, de Finetti-style theorems can often simplify the analysis in worst-case input scenarios for which the task exhibits some permutation-invariance symmetry, as they can allow for a reduction from an analysis on worst-case inputs to that of i.i.d. inputs. If further information is available on the inputs, it might be advantageous to reflect this information in the de Finetti reduction. In our work, we focus on a form of such constraint, based on the type of the input. This allows us to obtain a conceptually simple proof of a new de Finetti reduction for classical probability distributions, derived from elementary properties from the method of types. We apply our constrained de Finetti reduction to the compression of quantum interactive communication protocols with classical inputs, and prove that the prior-free quantum information cost equals the worst-case input amortized quantum communication cost.

quant-ph↗

arXiv2025

Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols

There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we study this relationship in the prior-free and interactive setting, where we provide an alternate proof for the result of Braverman [SIAM Review, vol. 59, no. 4, 2017], that the amortized communication complexity of simulating a prior-free interactive communication protocol, is equal to its prior-free information cost. While this is a known result, our approach addresses the need for a more natural proof of it. We also improve on the result by achieving round preservation, and using a bounded quantity of shared randomness. We do this by showing that the communicating parties can produce a reliable estimate of the joint type, or empirical distribution, of their inputs. This estimate is then used in our protocol for the prior-free reverse Shannon theorem with side information at the receiver. These results are then generalized to the interactive setting to obtain our main result.

cs.IT↗

arXiv2024

The Design and Implementation of a Quantum Information Science Undergraduate Program

Quantum information science is a burgeoning research field attracting vast public and private investment in the last decade. This quick rise has led to a talent gap, where there are more open positions than new graduates who can fill these roles. To meet this critical need, higher education has been challenged to react accordingly by assuring a flow of highly skilled individuals who must be trained quickly. We thus present how Université de Sherbrooke, in Quebec, Canada, responded by creating and launching an innovative undergraduate degree in quantum information science, aiming to address this gap by training quantum software developers in three and a half years. At the end of this program, they will be ready to join the quantum workforce. We detail the creative process leading to a coherent curriculum, as well as why the local ecosystem led to these choices. The guiding principles and lessons learned during the development of this interdepartmental and interfaculty degree are shared to inspire other quantum education institutions.

physics.ed-ph↗

arXiv2024

Improving Qubit Routing by Using Entanglement Mediated Remote Gates

Near-term quantum computers often have connectivity constraints, i.e. restrictions, on which pairs of qubits in the device can interact. Optimally mapping a quantum circuit to a hardware topology under these constraints is a difficult task. While numerous approaches have been proposed to optimize qubit routing, the resulting gate count and depth overheads of the compiled circuits remain high due to the short-range coupling of qubits in many near-term devices. Resource states, such as Bell or Einstein-Podolsky-Rosen (EPR) pairs, can be used to mediate operations that facilitate long-range interactions between qubits. In this work, we studied some of the practical trade-offs involved in using resource states for qubit routing. We developed a method that leverages an existing state-of-the-art compiler to optimize the routing of circuits with both standard gates and EPR mediated remote controlled-NOT gates. This was then used to compile different benchmark circuits for a square grid topology, where a fraction of the qubits are used to store EPR pairs. We demonstrate that EPR-mediated operations can substantially reduce the total number of gates and depths of compiled circuits when used with an appropriate optimizing compiler that accounts for practical overheads. Our results highlight the relevance of developing efficient compilation tools that can integrate EPR-mediated operations.

quant-ph↗

arXiv2023

One-shot quantum state redistribution and quantum Markov chains

We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.

quant-ph↗

arXiv2022

Augmented Index and Quantum Streaming Algorithms for DYCK(2)

We show how two recently developed quantum information theoretic tools can be applied to obtain lower bounds on quantum information complexity. We also develop new tools with potential for broader applicability, and use them to establish a lower bound on the quantum information complexity for the Augmented Index function on an easy distribution. This approach allows us to handle superpositions rather than distributions over inputs, the main technical challenge faced previously. By providing a quantum generalization of the argument of Jain and Nayak [IEEE TIT'14], we leverage this to obtain a lower bound on the space complexity of multi-pass, unidirectional quantum streaming algorithms for the DYCK(2) language.

quant-ph↗

arXiv2021

Incompressibility of classical distributions

In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $ρ$ drawn from a known ensemble (but without knowing what $ρ$ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of $ρ$. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assisted visible compression of mixed states wherein Alice knows what state is drawn. In this paper, we prove a general and robust lower bound on the achievable rate for ensembles of classical states, which holds even in the least demanding setting when Alice and Bob share free entanglement and a constant per-copy error is allowed. We apply the bound to a specific ensemble of only two states and prove a near-maximal separation (saturating the dimension bound in leading order) between the best achievable rate and the Holevo information for constant error. This also implies that the ensemble is incompressible -- compression does not reduce the communication cost by much. Since the states are classical, the observed incompressibility is not fundamentally quantum mechanical. We lower bound the difference between the achievable rate and the Holevo information in terms of quantitative limitations to clone the specimen or to distinguish the two classical states.

quant-ph↗

arXiv2020

Direct Sum Theorem for Bounded Round Quantum Communication Complexity

We prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact that information is a lower bound on the communication, and the fact that a direct sum property holds for quantum information complexity. We then give a protocol for compressing a single copy of a protocol down to its quantum information cost, up to terms depending on the number of rounds and the allowed increase in error. Two important tools to derive this protocol are a smooth conditional min-entropy bound for a one-shot quantum state redistribution protocol, and the quantum substate theorem of Jain, Radhakrishnan and Sen (FOCS'02) to transform this bound into a von Neumann conditional entropy bound. This result further establishes the newly introduced notions of quantum information cost and complexity as the correct quantum generalisations of the classical ones in the standard communication complexity setting. Finding such a quantum generalization of information complexity was one of the open problem recently raised by Braverman (STOC'12).

quant-ph↗

arXiv2020

Optical quantum communication complexity in the simultaneous message passing model

The communication cost of a classical protocol is typically measured in terms of the number of bits communicated for this determines the time required for communication during the protocol. Similarly, for quantum communication protocols, which use finite-dimensional quantum states, the communication cost is measured in terms of the number of qubits communicated. However, in quantum physics, one can also use infinite-dimensional states, like optical quantum states, for communication protocols. Communication cost measures based on counting the (equivalent) number of qubits transmitted during communication cannot be directly used to measure the cost of such protocols, which use infinite-dimensional states. Moreover, one cannot infer any physical property of infinite-dimensional protocols using such qubit based communication costs. In this paper, we provide a framework to understand the growth of physical resources in infinite-dimensional protocols. We focus on optical protocols for the sake of concreteness. The time required for communication and the energy expended during communication are identified as the important physical resources of such protocols. In an optical protocol, the time required for communication is determined by the number of time-bin modes that are transmitted from one party to another. The mean photon number of the messages sent determines the energy required during communication in the protocol. We prove a lower bound on the tradeoff between the growth of these two quantities with the growth of the problem size. We call such tradeoff relations optical quantum communication complexity relations.

quant-ph↗

arXiv2020

Erasable Bit Commitment from Temporary Quantum Trust

We introduce a new setting for two-party cryptography with temporarily trusted third parties. In addition to Alice and Bob in this setting, there are additional third parties, which Alice and Bob both trust to be honest during the protocol. However, once the protocol concludes, there is no guarantee over the behaviour of these third parties. It is possible that they collaborate and act adversarially. Our goal is to use these third parties to facilitate protocols which are impossible in two-party cryptography. We implement a variant of bit commitment in this setting, which we call erasable bit commitment. In this primitive, Alice has the choice of either opening or erasing her commitment after the commit phase. The ability to ask for an erasure allows Alice to ask the trusted parties to erase her commitment in case the trust period is about to expire. This erasure prevents a future coalition of the third parties and Bob from extracting any information about the commitment. However, this ability also makes erasable bit commitment weaker than the standard version of bit commitment. In addition to satisfying the security requirements of bit commitment, our protocol also does not reveal any information about the commitment to the third parties. Lastly, our protocol for this primitive requires a constant number of trusted third parties and can tolerate a small number of corrupt trusted parties as well as implementation errors.

quant-ph↗

arXiv2020

Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets

We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages, designed for a noiseless qudit channel over a $\mathrm{poly}(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2^{-Θ(nε)}$ and uses a qudit channel over the same alphabet $n\left(1+Θ\left(\sqrtε\right)\right)$ times, of which an $ε$ fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the $\sqrtε$ term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low $ε$.

quant-ph↗

arXiv2019

Noisy Interactive Quantum Communication

We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for eventual real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems. These are the first results concerning the quantum version of this problem, originally studied by Schulman in a classical setting (FOCS '92, STOC '93). We simulate a length $N$ quantum communication protocol by a length $O(N)$ protocol with arbitrarily small error. Under adversarial noise, our strategy can withstand, for arbitrarily small $ε> 0$, error rates as high as $1/2 -ε$ when parties pre-share perfect entanglement, but the classical channel is noisy. We show that this is optimal. We provide extension of these results in several other models of communication, including when also the entanglement is noisy, and when there is no pre-shared entanglement but communication is quantum and noisy. We also study the case of random noise, for which we provide simulation protocols with positive communication rates and no pre-shared entanglement over some quantum channels with quantum capacity $C_Q=0$, proving that $C_Q$ is in general not the right characterization of a channel's capacity for interactive quantum communication. Our results are stated for a general quantum communication protocol in which Alice and Bob collaborate, and these results hold in particular in the quantum communication complexity settings of the Yao and Cleve--Buhrman models.

quant-ph↗

arXiv2019

Quantum Insertion-Deletion Channels

We introduce a model of quantum insertion-deletion (insdel) channels. Insdel channels are meant to represent, for example, synchronization errors arising in data transmission. In the classical setting, they represent a strict generalization of the better-understood corruption error channels, and until recently, had mostly resisted effort toward a similar understanding as their corruption counterparts. They have received considerable attention in recent years. Very recently, Haeupler and Shahrasbi developed a framework, using what they call synchronisation strings, that allows one to turn insdel-type errors into corruption-type errors. These can then be handled by the use of standard error-correcting codes. We show that their framework can be extended to the quantum setting, providing a way to turn quantum insdel errors into quantum corruption errors, which can be handled with standard quantum error-correcting codes.

quant-ph↗

arXiv2018

Quantum Log-Approximate-Rank Conjecture is also False

In a recent breakthrough result, Chattopadhyay, Mande and Sherif [ECCC TR18-17] showed an exponential separation between the log approximate rank and randomized communication complexity of a total function $f$, hence refuting the log approximate rank conjecture of Lee and Shraibman [2009]. We provide an alternate proof of their randomized communication complexity lower bound using the information complexity approach. Using the intuition developed there, we derive a polynomially-related quantum communication complexity lower bound using the quantum information complexity approach, thus providing an exponential separation between the log approximate rank and quantum communication complexity of $f$. Previously, the best known separation between these two measures was (almost) quadratic, due to Anshu, Ben-David, Garg, Jain, Kothari and Lee [CCC, 2017]. This settles one of the main question left open by Chattopadhyay, Mande and Sherif, and refutes the quantum log approximate rank conjecture of Lee and Shraibman [2009]. Along the way, we develop a Shearer-type protocol embedding for product input distributions that might be of independent interest.

quant-ph↗

arXiv2018

Practical Quantum Appointment Scheduling

We propose a protocol based on coherent states and linear optics operations for solving the appointment-scheduling problem. Our main protocol leaks strictly less information about each party's input than the optimal classical protocol, even when considering experimental errors. Along with the ability to generate constant-amplitude coherent states over two modes, this protocol requires the ability to transfer these modes back-and-forth between the two parties multiple times with low coupling loss. The implementation requirements are thus still challenging. Along the way, we develop new tools to study quantum information cost of interactive protocols in the finite regime.

quant-ph↗

arXiv2017

The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting

In the context of two-party interactive quantum communication protocols, we study a recently defined notion of quantum information cost (QIC), which possesses most of the important properties of its classical analogue. Although this definition has the advantage to be valid for fully quantum inputs and tasks, its interpretation for classical tasks remained rather obscure. Also, the link between this new notion and other notions of information cost for quantum protocols that had previously appeared in the literature was not clear, if existent at all. We settle both these issues: for quantum communication with classical inputs, we provide an alternate characterization of QIC in terms of information about the input registers, avoiding any reference to the notion of a purification of the classical input state. We provide an exact operational interpretation of this alternative characterization as the sum of the cost of transmitting information about the classical inputs and the cost of forgetting information about these inputs. To obtain this characterization, we prove a general lemma, the Information Flow Lemma, assessing exactly the transfer of information in general interactive quantum processes. Furthermore, we clarify the link between QIC and IC of classical protocols by simulating quantumly classical protocols. Finally, we apply these concepts to argue that any quantum protocol that does not forget information solves Disjointness on n-bits in Omega (n) communication, completely losing the quadratic quantum speedup. This provides a specific sense in which forgetting information is a necessary feature of interactive quantum protocols. We also apply these concepts to prove that QIC at zero-error is exactly n for the Inner Product function, and n (1 - o(1)) for a random Boolean function on n+n bits.

quant-ph↗

arXiv2016

Exponential Separation of Quantum Communication and Classical Information

We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that these two complexity measures are incomparable. As classical information complexity is an upper bound on quantum information complexity, which in turn is equal to amortized quantum communication complexity, our work implies that a tight direct sum result for distributional quantum communication complexity cannot hold. The function we use to present such a separation is the Symmetric k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057], whose classical communication complexity is exponentially larger than its classical information complexity. In this paper, we show that the quantum communication complexity of this function is polynomially equivalent to its classical communication complexity. The high-level idea behind our proof is arguably the simplest so far for such an exponential separation between information and communication, driven by a sequence of round-elimination arguments, allowing us to simplify further the approach of Rao and Sinha. As another application of the techniques that we develop, we give a simple proof for an optimal trade-off between Alice's and Bob's communication while computing the related Greater-Than function on n bits: say Bob communicates at most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when allowing pre-shared entanglement. We also present a classical protocol achieving this bound.

quant-ph↗

arXiv2016

Quantum Advantage on Information Leakage for Equality

We prove a lower bound on the information leakage of any classical protocol computing the equality function in the simultaneous message passing (SMP) model. Our bound is valid in the finite length regime and is strong enough to demonstrate a quantum advantage in terms of information leakage for practical quantum protocols. We prove our bound by obtaining an improved finite size version of the communication bound due to Babai and Kimmel, relating randomized communication to deterministic communication in the SMP model. We then relate information leakage to randomized communication through a series of reductions. We first provide alternative characterizations for information leakage, allowing us to link it to average length communication while allowing for shared randomness (pairwise, with the referee). A Markov inequality links this with bounded length communication, and a Newman type argument allows us to go from shared to private randomness. The only reduction in which we incur more than a logarithmic additive factor is in the Markov inequality; in particular, our compression method is essentially tight for the SMP model with average length communication.

cs.CC↗