arXiv subjects

Mark Hillery

Publications and source records attributed to Mark Hillery.

At least 19 recordsLinked to original sources

arXiv2026

Detection of patterns in a discrete-outcome sensor network

A discrete outcome quantum sensor network is one in which we are only interested in which detectors are activated. This can be studied in either the strong or weak interaction regime. If the detectors interact strongly with the environment, it is possible to definitely find which ones were activated. If the interaction is weaker, there is a possibility of making an error, and the object is to minimize the probability of this happening. Here we will be interested in this weaker interaction regime. We will also assume that only certain patterns of detectors will be activated, different patterns being translated versions of a fundamental one. Our object will be to find which pattern has been activated. We will look at both one and two-dimensional detector arrays and make use of techniques from minimum-error state discrimination.

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arXiv2026

Experimental quantum state learning with pairs of photons

Tomography allows one to estimate the density matrix describing the state an ensemble of quantum systems are prepared in (for example, polarization tomography determines the polarization state of a beam of identically prepared photons). In general, it is not possible to uniquely decompose the density matrix into its pure state components. Agarwal et al. proposed a protocol which, for a mixture composed of any two pure states of a qubit (with arbitrary probabilities), allows an observer to infer not only the density matrix but the identity of those specific pure states and their weights - the additional requirement being that the qubits arrive in pairs, where both qubits in each pair are in the same state. We experimentally demonstrate this learning-from-pairs concept using photons in the polarization degree of freedom. We use tomography to measure a sequence of single photons and make use of their time-of-arrival information to 'pair up' the photons after the measurement. From here we are able to infer the photons' polarization states and their respective probabilities, and we demonstrate this for various different choices of polarization states and ratios. Finally, we investigate our ability to discriminate between two equal mixtures of distinct pairs of orthogonal polarization states. We find that on the order of approx. 10e4 photons is typically enough to achieve tomography fidelities of approximately 0.9999. This is sufficient to discriminate between two different preparations of the same mixed state, differing by angles of less than 5 degrees between the pure states used in the two preparations.

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arXiv2026

Quantum-Enhanced Zero-Error Communication and Storage under Positional Uncertainty

Permutation channels model communication and storage scenarios in which the positional identity of the physical carriers is partially or completely lost, so that the transmitted information is only accessible up to an unknown reordering. Here we show that quantum mechanics can dramatically enhance zero-error communication through such channels. For cyclic reorderings of $n$ $d$-level systems, and in the absence of positional metadata, the number of classical zero-error messages scales asymptotically as $d^n/n$, whereas quantum protocols can fully recover the identity-channel value $d^n$. Ancilla-assisted protocols further increase this number to $d^{2n}/n$, enabling dense coding under positional uncertainty. We also analyze dihedral permutation channels and derive general P\'olya-like formulas for the number of distinguishable messages in a broad class of permutation groups. Finally, for the symmetric group $S_n$, corresponding to complete scrambling of the information carriers, the number of distinguishable messages scales as $n^{d-1}$ classically, compared with $n^{d(d+1)/2-1}$ for quantum protocols and $n^{d^2-1}$ in the ancilla-assisted setting. Our results establish a fundamental quantum advantage for communication and storage under positional uncertainty.

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arXiv2026

Conditions for 3-partite and 4-partite genuine entanglement

A system of three or four particle can be entangled in a number of different ways. It may be the case that only subsets of the particles are entangled, and these subsets are not entangled with each other. It may also be the case that the state is the sum of states in which entanglement only exists within subsets. If this is not the case, the state is said to be genuinely entangled. GHZ states, for example, are genuinely entangled. Deciding whether a state is genuinely entangled is not simple, but conditions do exist to detect it. Here we would like to propose additional sufficient conditions based on one for bipartite entanglement.

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arXiv2025

Quantum Advantage in Identifying the Parity of Permutations with Certainty

We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is limited to random guessing. Quantum mechanics does it with certainty with as few as $\lceil \sqrt{n}\, \rceil$ distinguishable states per particle, thanks to entanglement. Below this threshold, not even quantum mechanics helps: both classical and quantum success are limited to random guessing. For small $n$, we provide explicit expressions for states that ensure perfect parity identification. We also assess the minimum entanglement these states need to carry, finding it to be close to maximal, and even maximal in some cases. The task requires no oracles or contrived setups and provides a simple, rigorous example of genuine quantum advantage.

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arXiv2025

Interference and Measurement: Changing amplitude phase information to amplitude magnitude information

There are quantum procedures that encode the solutions to a problem in the phases of quantum amplitudes. This happens in some quantum optimization algorithms in which the value of a function to be maximized or minimized is represented by a phase. An example of this is the QAOA algorithm for the MaxCut problem in which one encodes the number of edges connecting the sets resulting from a partition of the vertices of a graph into phases of amplitudes of a quantum state. Another is the minimum vertex cover problem in which the number of edges included in the cover is encoded in phases. Here we want to see what can be done if we only use simple aspects of quantum mechanics, interference and measurement, to manipulate the magnitudes of the amplitudes whose phases encode the relevant information. The idea is to use constructive interference to enhance the amplitudes that contain useful information and destructive interference to suppress those that do not. We examine examples, both analytically and numerically. We also show how the results of sequences of measurements can be used to gain information about the landscape of solutions.

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arXiv2024

State learning from pairs of states

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning -- or quantum state estimation. A problem is that, without more information, all that can be determined is the density matrix of the sequence and, in general, density matrices can be decomposed into pure states in many different ways. To solve the problem, additional information, either classical or quantum, is required. We show that if an additional copy of each qubit is supplied -- that is, one receives pairs of qubits, both in the same state, rather than single qubits -- the task can be accomplished. This is possible because the mixed two-qubit state has a unique decomposition into pure product states. For illustration, we simulate numerically the symmetric, informationally complete measurement of a sequence of qubit pairs and show that the unknown states and their respective probabilities of occurrence can be inferred from the data with high accuracy. Finally, we propose an experiment that employs a product measurement and can be realized with existing technology, and we demonstrate how the data tell us the states and their probabilities. We find that it is enough to detect a few thousand qubit pairs.

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arXiv2024

Discrete-outcome sensor networks: Multiple detection events and grouping detectors

Quantum sensor networks have often been studied in order to determine how accurately they can determine a parameter, such as the strength of a magnetic field, at one of the detectors. A more coarse-grained approach is to try to simply determine whether a detector has interacted with a signal or not, and which detector it was. Such discrete-outcome quantum sensor networks, discrete in the sense that we are seeking answers to yes-no questions, are what we study here. One issue is what is a good initial state for the network, and, in particular, should it be entangled or not. Earlier we looked at the case when only one detector interacted, and here we extend that study in two ways. First, we allow more that one detector to interact, and second, we examine the effect of grouping the detectors. When the detectors are grouped we are only interested in which group contained interacting detectors and not in which individual detectors within a group interacted. We find that in the case of grouping detectors, entangled initial states can be helpful.

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arXiv2024

Can a qudit carry more information than a dit?

Conventional wisdom suggests that within a fixed preparation-measurement setup, a qubit system offers no advantage over a bit. This indeed holds true when considering the standard communication and the famous Holevo bound then formalizes the statement that one qubit can encode at most one bit of information. However, there exist subtle differences between these two physical systems that, when properly exploited, can be converted into practical applications. We begin by discussing the similarities between qudits and dits as information carriers. Then we recall a general framework for communication tasks and review some differences that qudits and dits have. In the end, we present a simple communication application that utilizes the quantum character of the qubit.

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arXiv2023

Two entanglement conditions and their connection to negativity

We examine two conditions that can be used to detect bipartite entanglement, and show that they can be used to provide lower bounds on the negativity of states. We begin with two-qubit states, and then show how what was done there can be extended to more general states. The resulting bounds are then studied by means of a number of examples. We also show that if one has some knowledge of the Schmidt vectors of a state, better bounds can be found.

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arXiv2023

Lower bound on phase noise of classical states

An uncertainty relation for the number and phase of a single-mode field state is derived. It is then used to find a lower bound on the phase noise of a classical state. Any state that violates this condition is nonclassical. An example of such a nonclassical state is presented. Because a nonclassical state can have less phase noise than a classical state with the same average photon number, nonclassical states can play a role in the measurement of small phase shifts.

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arXiv2023

Optimizing Initial State of Detector Sensors in Quantum Sensor Networks

In this paper, we consider a network of quantum sensors, where each sensor is a qubit detector that "fires," i.e., its state changes when an event occurs close by. The change in state due to the firing of a detector is given by a unitary operator which is the same for all sensors in the network. Such a network of detectors can be used to localize an event, using a protocol to determine the firing sensor which is presumably the one closest to the event. The determination of the firing sensor can be posed as a Quantum State Discrimination problem which incurs a probability of error depending on the initial state and the measurement operator used. In this paper, we address the problem of determining the optimal initial global state of a network of detectors that incur a minimum probability of error in determining the firing sensor. For this problem, we derive necessary and sufficient conditions for the existence of an initial state that allows for perfect discrimination, i.e., zero probability of error. Using insights from this result, we derive a conjectured optimal solution for the initial state, provide a pathway to prove the conjecture, and validate the conjecture empirically using multiple search heuristics that seem to perform near-optimally.

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arXiv2023

Broadcasting single-qubit and multi-qubit-entangled states: authentication, cryptography, and distributed quantum computation

Quantum entanglement assisted with measurements provides various pathways to communicate information to parties within a network. In this work, we generalize a previous broadcasting protocol and present schemes to broadcast product and multi-partite entangled quantum states, where in the latter case the sender can remotely add phase gates or abort distributing the states. We first focus on the broadcasting of product quantum states in a network, and generalize the basic protocol to include an arbitrary basis rotation and allow for multiple receivers and senders. We show how to add and delete senders from the network. The generalization also includes the case where a phase to be applied to the broadcast states is not known in advance but is provided to a sender encoded in another quantum state. Applications of broadcasting product states include authentication and three-state quantum cryptography. In the second part, we study the distribution of a single multi-qubit state shared among several receivers entangled with multi-qubit phase gates, which includes the graph states as an example. We show that by coordinating with the sender, the receivers can assist in performing remote, distributed measurement-based quantum computation with the Pauli X basis measurement alone. As another application of this, we discuss the distribution of the multi-qubit Greenberger-Horne-Zeilinger state.

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arXiv2022

Discrete outcome quantum sensor networks

We model a quantum sensor network using techniques from quantum state discrimination. The interaction between a qubit detector and the environment is described by a unitary operator, and we will assume that at most one detector does interact. The task is to determine which one does or if none do. This involves choosing an initial state of the detectors and a measurement. We consider global measurements in which all detectors are measured simultaneously. We find that an entangled initial state can improve the detection probability, but this advantage decreases as the number of detectors increases.

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arXiv2022

Broadcast of a restricted set of qubit and qutrit states

The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, probabilistically sending an unknown qubit state to two receivers, sending different qubit states to two receivers, and sending qutrit states to two receivers. Finally, we discuss some applications of these protocols.

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arXiv2021

Optimal linear optical discrimination of Bell-like states

Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillas, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50% we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprised of single photon detectors and beam splitters with input state-dependent parameters that achieves optimal discrimination in the Bell-like case.

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arXiv2021

Partial particle and wave information and weak duality games

Duality games are a way of looking at wave-particle duality. In these games. Alice and Bob together are playing against the House. The House specifies, at random, which of two sub-games Alice and Bob will play. One game, Ways, requires that they obtain path information about a particle going through an $N$-path interferometer and the other, Phases, requires that they obtain phase information. In general, because of wave-particle duality, Alice and Bob cannot always win the overall game. However, if the required amount of path and phase information is not too great, for example specifying a set of paths or phases, one of which is the right one, then they can always win. Here we study examples of duality games that can always be won, and develop a wave-particle duality relation expressed only in terms of mutual information to help analyze these games.

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arXiv2021

Average concurrence and entanglement swapping

We study the role of average concurrence in entanglement swapping in quantum networks. We begin with qubit pure states, and there is a very simple rule governing the propagation of average concurrence in multiple swaps. We look at examples of mixed qubit states, and find the relation for pure states gives an upper bound on what is possible with mixed states. We then move on to qudits, where we make use of the I-concurrence. Here the situation is not as simple as for qubits, but in some cases relatively straightforward results can be obtained.

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