arXiv subjects

James Fullwood

Publications and source records attributed to James Fullwood.

At least 19 recordsLinked to original sources

arXiv2026

On the entropy of a pseudo-density matrix

The pseudo-density matrix (PDM) formalism naturally extends the notion of density operator to the spatiotemporal domain. While PDMs are Hermitian and of unit trace, they admit negative eigenvalues when encoding temporal correlations unattainable for spacelike separated systems. Consequently, there have been various approaches to extending the von~Neumann entropy---which is only defined for positive operators---to PDMs. Here, we prove that there exists a unique extension of the von~Neumann entropy functional to Hermitian matrices of unit trace satisfying two simple assumptions: unitary invariance and strong additivity with respect to affine combinations within the interval $[-1,1]$, which we prove contains the eigenvalues of a PDM. We also prove that this unique extension of von~Neumann entropy to PDMs is subadditive for single qubit dynamics, and we analyze its behavior in a number of examples.

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arXiv2026

Quantum information loss

We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss quantifies Bob's inability to retrodict with certainty which state Alice sent through the channel. By minimizing this measure over all possible pure state ensemble decompositions of a fixed state $\rho$, and over all POVMs on the output of a channel $\mathcal{E}$, we arrive at an intrinsic notion of information loss for any state-channel pair $(\rho,\mathcal{E})$. We show that the vanishing of information loss with respect to all states supported on a fixed codespace $\mathcal{H}_{\text{code}}$ is equivalent to a condition we term \emph{universal pristineness}, which ensures that orthogonal pure states in $\mathcal{H}_{\text{code}}$ get sent via the channel $\mathcal{E}$ to possibly mixed states whose supports are orthogonal. Moreover, we prove universal pristineness is equivalent to the Knill-Laflamme conditions in quantum error correction, which are necessary and sufficient for the existence of a perfect recovery channel for all states supported on $\mathcal{H}_{\text{code}}$. As an application, we apply our framework to the Hayden-Preskill model of black hole evaporation, demonstrating that the evaporation channel becomes asymptotically universally pristine, thereby providing a purely channel-theoretic formulation of Page-time information retrieval.

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arXiv2026

Operational time-reversal symmetry for unital qubit channels

The Bayesian inverse of a quantum channel $\mathcal{E}$ is a channel $\mathcal{F}$ in the reverse direction of $\mathcal{E}$ that yields time-symmetric correlations for sequential measurements performed on open quantum systems. Such an operational form of time-reversal symmetry for open quantum systems is quite remarkable, as the dynamics of open quantum systems are inherently irreversible due to system-environment interactions. Similar to the Petz map, a Bayesian inverse $\mathcal{F}$ is defined with respect to a fiducial reference state $ρ$ for the channel $\mathcal{E}$. However, Bayesian inverses do not always exist, and it is often a non-trivial task to determine the set of states $ρ$ for which a Bayesian inverse of $\mathcal{E}$ exists. In this work, we solve the general problem of quantum Bayesian inversion for unital channels acting on a single qubit. Our analysis is streamlined by demonstrating that finding a Bayesian inverse for a unital qubit channel may be reduced to finding a Bayesian inverse of a Pauli channel, which is simply a mixture of unitary channels associated with the Pauli matrices. As such, we provide a complete description of when operational time-reversal symmetry is attainable for sequential measurements of a single qubit in the presence of unital noise.

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arXiv2026

On Lorentzian symmetries of quantum information

A foundational result in relativistic quantum information theory due to Peres, Scudo, and Terno, is that von Neumann entropy is not Lorentz invariant. Motivated by the "It from Qubit" paradigm, here we show that Lorentzian symmetries of quantum information emerge naturally in a pre-spacetime setting, without any reference to external variables such as position or momentum. In particular, we derive the natural action of the restricted Lorentz group $\text{SO}^+(1,3)$ on the internal degrees of freedom of a single qubit from a simple, information-theoretic principle we refer to as preservation of linear entropy. It is then shown that the Lorentz invariance of the linear entropy of a relativistic qubit is a special case of a much more general phenomenon, namely, that any spectral invariant of an operator we term the '$W$-matrix' is an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant scalar. Consequently, the linear $n$-partite quantum mutual information is shown to be an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant for all $n$-qubit states. Finally, we show that the correlation function associated with a pair of qubits in the singlet state yields the Minkowski metric on the space of qubit observables, whose symmetry group is the full Lorentz group $\text{SO}(1,3)$. In accordance with the "It from Qubit" paradigm, our results thus establish the natural emergence of relativistic spacetime structure from intrinsic properties of quantum information.

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arXiv2026

The Born rule as a natural transformation of functors

In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In particular, we show that given a fixed quantum system, there exists an explicit bijection from the set of density operators on the associated Hilbert space to the set of natural transformations between the canonical measurement and probability functors associated with the system, which formalize the way in which quantum effects (i.e., POVM elements) and their associated probabilities are additive with respect to a coarse-graining of measurements.

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arXiv2026

Multipartite quantum states over time from two fundamental assumptions

The theory of quantum states over time extends the density operator formalism into the temporal domain, providing a unified of treatment of timelike and spacelike separated systems in quantum theory. Although recent results have characterized quantum states over time involving two timelike separated systems, it remains unclear how to consistently extend the notion of quantum states over time to multipartite temporal scenarios, such as those considered in studies of Leggett-Garg inequalities. In this Letter, we show that two simple assumptions uniquely single out the Markovian multipartite extension of bipartite quantum states over time, namely, linearity in the initial state and a quantum analog of conditionability for multipartite probability distributions. As a direct consequence of our result, we establish a canonical correspondence between multipartite QSOTs and Kirkwood-Dirac type quasiprobability distributions, which we show opens up the possibility of experimentally verifying the temporal correlations encoded in QSOTs via the recent experimental technique of simulating quasiprobability known as quantum snapshotting.

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arXiv2026

The spatiotemporal Born rule is quasiprobabilistic

Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint probabilities associated with measurements performed in sequence are defined in terms of the state-update rule. In this work, we show that one obtains a more unified perspective of space and time in quantum theory by embracing a quasiprobabilistic description of sequential measurements. More precisely, we show that there exists a unique \emph{pseudo}-density operator encoding canonical quasiprobabilities associated with sequential measurements in precisely the same manner that a density operator encodes joint probabilities associated with spacelike separated measurements, thus providing a natural extension of the Born rule into the temporal domain. As an application, we show how such a spatiotemporal Born rule combined in conjunction with a quantum Bayes' rule yields an operational notion of time-reversal symmetry for sequential measurements on an \emph{open} quantum system.

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arXiv2025

On small perturbations of coherent information

Quantum capacity quantifies the amount of quantum information that can be transmitted by a quantum channel with an arbitrary small probability of error. Mathematically, the quantum capacity is given by an asymptotic formula involving the one-shot quantum capacity of the associated channel, which, due to purely quantum effects such as superadditivity of one-shot quantum capacity, is rarely computable. The one-shot quantum capacity is mathematically characterized in terms of optimizing an entropic quantity referred to as coherent information over all possible input states of a channel, the computation of which also tends to be intractable due to the difficulty of optimizing the coherent information. In this work, we develop perturbative methods for analyzing the behavior of coherent information of a quantum channel with respect to small perturbations of the input state. By doing so, we are able to derive three general criteria for determining whether an input state yields suboptimal coherent information. We then show how our criteria yield sufficient conditions for superadditivity of one-shot quantum capacity, and also for detecting a positive gap between one-shot private capacity and one-shot quantum capacity. The utility of our criteria is illustrated through examples, which yield new results regarding the one-shot quantum capacity of qubit depolarizing channels, Pauli channels and dephrasure channels.

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arXiv2025

On Dirac-type correlations

Quantum correlations often defy an explanation in terms of fundamental notions of classical physics, such as causality, locality, and realism. While the mathematical theory underpinning quantum correlations between spacelike separated systems has been well-established since the 1930s, the mathematical theory for correlations between non-spacelike separated systems is much less developed. In this work, we develop the theory of what we refer to as "local-density operators", which we view as joint states for possibly non-spacelike separated quantum systems. Local-density operators are unit trace operators whose marginals are genuine density operators, which we show not only subsumes the notion of density operator, but also several extensions of the notion of density operator into the spatiotemporal domain, such as pseudo-density operators and quantum states over time. More importantly, we prove a result which establishes a one-to-one correspondence between local-density operators and what we refer to as "Dirac measures", which are complex-valued measures on the space of separable projectors associated with two quantum systems. In the case that one of the systems is the trivial quantum system with a one-dimensional Hilbert space, our result recovers the fundamental result known as Gleason's Theorem, which implies that the Born rule from quantum theory is the only way in which one may assign probabilities to the outcomes of measurements performed on quantum systems in a non-contextual manner. As such, our results establish a direct generalization of Gleason's Theorem to measurements performed on possibly non-spacelike separated systems, thus extending the mathematical theory of quantum correlations across space to quantum correlations across space and time.

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arXiv2025

Pindrop it! Audio and Visual Deepfake Countermeasures for Robust Detection and Fine Grained-Localization

The field of visual and audio generation is burgeoning with new state-of-the-art methods. This rapid proliferation of new techniques underscores the need for robust solutions for detecting synthetic content in videos. In particular, when fine-grained alterations via localized manipulations are performed in visual, audio, or both domains, these subtle modifications add challenges to the detection algorithms. This paper presents solutions for the problems of deepfake video classification and localization. The methods were submitted to the ACM 1M Deepfakes Detection Challenge, achieving the best performance in the temporal localization task and a top four ranking in the classification task for the TestA split of the evaluation dataset.

cs.CV↗

arXiv2025

Partial transpose as a space-time swap

While the partial transpose operation appears in many fundamental results in quantum theory -- such as the Peres-Horodecki criterion for entanglement detection -- a physical interpretation of the partial transpose is lacking. In this work, we show that a partial transpose of a bipartite density operator is a two-time pseudo-density operator, which by definition encodes temporal correlations associated with two-point sequential measurement scenarios. As such, it follows that partial transposition admits a precise physical interpretation as mapping spatial correlations to temporal correlations, thus swapping the roles of space and time for bipartite quantum systems. For maximally entangled qubits, we show that partial transposition maps spatial correlations which violate Bell inequalities to causal correlations which cannot be replicated by spacelike separated systems, thus further solidifying the interpretation of partial transpose as a space-time swap. As it is known that gravitational effects swap the roles of space and time inside a black hole, our results suggest that at a quantum mechanical level, a traversal of a black hole's event horizon by a bipartite quantum system may be described by a partial transpose.

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arXiv2025

Quantum dynamics as a pseudo-density matrix

While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently it was emphasized in the work of Fitzsimons, Jones and Vedral that if such a state over time is to encode not only spatial but also temporal correlations which exist within a quantum dynamical process, then it should be represented not by a density matrix, but rather, by a pseudo-density matrix. A pseudo-density matrix is a hermitian matrix of unit trace whose marginals are density matrices, and in this work, we make use a factorization system for quantum channels to associate a pseudo-density matrix with a quantum system which is to evolve according to a finite sequence of quantum channels. We then view such a pseudo-density matrix as the quantum analog of a local patch of spacetime, and we make an in-depth mathematical analysis of such quantum dynamical pseudo-density matrices and the properties they satisfy. We also show how to explicitly extract quantum dynamics from a given pseudo-density matrix, thus solving an open problem posed in the literature.

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arXiv2025

Operator representation of spatiotemporal quantum correlations

While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, there does not exist an analogous operator representing general quantum correlations across space and time. This is in stark contrast to the case of classical random variables, which make no distinction between spacelike and timelike correlations. Despite this, we show that spatiotemporal correlations between light-touch observables (i.e., observables whose eigenvalues are all equal in magnitude) admit a unique operator representation for arbitrary timelike-separated quantum systems. A special case of our result reproduces generalized Pauli observables and pseudo-density matrices, which have, up until now, only been defined for multi-qubit systems. In the case of qutrit systems, we use our results to illustrate an intriguing connection between light-touch observables and symmetric, informationally complete, positive operator-valued measures (SIC-POVMs).

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arXiv2025

A diagrammatic formulation of local realism

Given two parties performing experiments in separate laboratories, we provide a diagrammatic formulation of what it means for the joint statistics of their experiments to satisfy local realism. In particular, we show that the principles of locality and realism are both captured by a single commutative diagram in the category of probability-preserving maps between finite probability spaces, and we also show that an assumption of such a diagrammatic formulation of local realism implies the standard CHSH inequality associated with dichotomic random variables. As quantum theory is known not to satisfy local realism, our formulation of local realism in terms of commutative diagrams provides yet another way in which the notion of non-commutativity plays a fundamental role in quantum theory. We note that we do not assume any prior knowledge of category theory or quantum theory, as this work is intended for philosophers, mathematicians and physicists alike.

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arXiv2025

Geometry from quantum temporal correlations

In this work, we show how Euclidean 3-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal correlations which give rise to geometry are independent of the initial state of the qubit, which we show enables an observer to extract geometric data from sequential measurements without the observer having any knowledge of initial conditions. Such results suggest the plausibility that space itself may emerge from quantum temporal correlations, and we formulate a toy model of such a hypothetical phenomenon.

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arXiv2024

Quantum Mutual Information in Time

While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual information between two random variables is well-defined irrespective of whether or not the variables are separated in space or separated in time. Motivated by this disparity between the classical and quantum mutual information, we employ the pseudo-density matrix formalism to define a simple extension of quantum mutual information into the time domain. As in the spatial case, we show that such a notion of quantum mutual information in time serves as a natural measure of correlation between timelike-separated systems, while also highlighting ways in which quantum correlations distinguish between space and time. We also show how such quantum mutual information is time-symmetric with respect to quantum Bayesian inversion, and then we conclude by showing how mutual information in time yields a Holevo bound for the amount of classical information that may be extracted from sequential measurements on an ensemble of quantum states.

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arXiv2024

Time-symmetric correlations for open quantum systems

Two-time expectation values of sequential measurements of dichotomic observables are known to be time symmetric for closed quantum systems. Namely, if a system evolves unitarily between sequential measurements of dichotomic observables $\mathscr{O}_{A}$ followed by $\mathscr{O}_{B}$, then it necessarily follows that $\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle=\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$, where $\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle$ is the two-time expectation value corresponding to the product of the measurement outcomes of $\mathscr{O}_{A}$ followed by $\mathscr{O}_{B}$, and $\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$ is the two-time expectation value associated with the time reversal of the unitary dynamics, where a measurement of $\mathscr{O}_{B}$ precedes a measurement of $\mathscr{O}_{A}$. In this work, we show that a quantum Bayes' rule implies a time symmetry for two-time expectation values associated with open quantum systems, which evolve according to a general quantum channel between measurements. Such results are in contrast with the view that processes associated with open quantum systems -- which may lose information to their environment -- are not reversible in any operational sense. We give an example of such time-symmetric correlations for the amplitude-damping channel, and we propose an experimental protocol for the potential verification of the theoretical predictions associated with our results.

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arXiv2024

General Communication Enhancement via the Quantum Switch

Recent studies have shown that quantum information may be effectively transmitted by a finite collection of completely depolarizing channels in a coherent superposition of different orders, via an operation known as the quantum $\tt SWITCH$. Such results are quite remarkable, as completely depolarizing channels taken in isolation and in a definite order can only output white noise. For general channels however, little is known about the potential communication enhancement provided by the quantum $\tt SWITCH$. In this Letter, we define an easily computable quantity $\mathcal{P}_n$ associated with the quantum ${\tt SWITCH}$ of $n$ copies of a fixed channel, and we conjecture that $\mathcal{P}_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $\tt SWITCH$. In support of our conjecture, we derive a simple analytic expression for the classical capacity of the quantum $\tt SWITCH$ of $n$ copies of an arbitrary Pauli channel in terms of the quantity $\mathcal{P}_n$, which we then use to show that our conjecture indeed holds in the space of all Pauli channels. Utilizing such results, we then formulate a communication protocol involving the quantum $\tt SWITCH$ which enhances the private capacity of the BB84 channel.

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