arXiv subjects

Ray Ganardi

Publications and source records attributed to Ray Ganardi.

15 recordsLinked to original sources

arXiv2026

Catalytic advantage in asymptotic entanglement manipulation

Entanglement is a key quantum resource in various quantum protocols, with a rich set of laws governing its manipulation. In this context, catalysis refers to the possibility of an auxiliary state that enables a previously forbidden manipulation, while being completely returned at the end. While the catalytic setting has been thoroughly examined in the single-copy regime, much less is known in the asymptotically many copy regime. In this work, we focus on the entanglement cost of preparing asymptotically many copies of a given state exactly. We show that catalysis can significantly lower the exact entanglement cost by constructing an explicit catalytic protocol. Additionally, these findings generalize readily to other resource theories, showing a general catalytic advantage in the resource dilution task.

quant-ph↗

arXiv2026

Manipulating heterogeneous quantum resources over a network

Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic. In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so different resources coexist and interact. Yet, resource theories have mostly treated each resource in isolation, and a general theory for manipulation in such distributed settings has been lacking. We develop a unified framework for composite quantum resource theories that describes distributed networks of locally constrained parties. We formulate natural axioms a composite theory should satisfy to respect the local structure, and from these axioms derive fundamental bounds on resource manipulation that hold universally, independent of the particular network characteristics. We apply our results to central operational tasks, including resource conversion and assisted distillation, and introduce new methods to construct new resource monotones from this setup. Our framework further reveals previously unexplored phenomena in the remote certification of quantum resources. Together, these results establish foundational laws for distributed quantum resource manipulation across diverse physical platforms.

quant-ph↗

arXiv2024

Catalytic channels are the only noise-robust catalytic processes

Catalysis refers to the possibility of enabling otherwise inaccessible quantum state transitions by supplying an auxiliary system, provided that the auxiliary is returned to its initial state at the end of the protocol. We show that previous studies on catalysis are largely impractical, because even small errors in the system's initial state can irreversibly degrade the catalyst. To overcome this limitation, we introduce robust catalytic transformations and explore the fundamental extent of their capabilities. We demonstrate that robust catalysis is closely tied to the property of resource broadcasting. In particular, in completely resource non-generating theories, robust catalysis is possible if and only if resource broadcasting is possible. We develop a no-go theorem under a set of general axioms, demonstrating that robust catalysis is unattainable for a broad class of quantum resource theories. However, surprisingly, we also identify thermodynamical scenarios where maximal robust catalytic advantage can be achieved. Our approach clarifies the practical prospects of catalytic advantage for a wide range of quantum resources, including entanglement, coherence, thermodynamics, magic, and imaginarity.

quant-ph↗

arXiv2024

Correlations and signaling in the Schr\"{o}dinger-Newton model

The Schr\"odinger--Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While there are many studies on the phenomenology of single particles, correlation dynamics in multipartite systems is largely unexplored. Here, we show that the Schr\"odinger--Newton interactions preserve the product form of the initial state of a many-body system, yet on average agreeing with classical mechanics of continuous mass distributions. This leads to a simple test of the model, based on verifying bipartite gravitational evolution towards non-product states. We show using standard quantum mechanics that, with currently accessible single-particle parameters, two masses released from harmonic traps get correlated well before any observable entanglement is accumulated. Therefore, the Schr\"odinger--Newton model can be tested with setups aimed at observation of gravitational entanglement with significantly relaxed requirements on coherence time. We also present a mixed-state extension of the model that avoids superluminal signaling.

quant-ph↗

arXiv2024

Second Law of Entanglement Manipulation with Entanglement Battery

A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic regime, mirroring the reversible nature of Carnot cycles in classical thermodynamics. While a conclusive proof of this conjecture has been missing so far, earlier studies have excluded reversible entanglement manipulation in various settings. In this work, we show that arbitrary mixed state entanglement transformations can be made reversible under local operations and classical communication, when assisted by an entanglement battery--an auxiliary quantum system that stores and supplies entanglement in a way that ensures no net entanglement is lost. In particular, the rate of transformation in the asymptotic limit can be quantitatively expressed as a ratio of entanglement present within the quantum states involved. Our setting allows to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a ``second law'' of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.

quant-ph↗

arXiv2023

Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement

Quantum thermodynamics and quantum entanglement represent two pivotal quantum resource theories with significant relevance in quantum information science. Despite their importance, the intricate relationship between these two theories is still not fully understood. Here, we delve into the interplay between entanglement and thermodynamics, particularly in the context of local cooling processes. We introduce and develop the framework of Gibbs-preserving local operations and classical communication. Within this framework, we explore strategies enabling remote parties to effectively cool their local systems to the ground state. Our analysis is centered on scenarios where only a single copy of a quantum state is accessible, with the ideal performance defined by the highest possible fidelity to the ground state achievable under these constraints. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. In this context, we establish a powerful link between the efficiency of local purity extraction and the degree of entanglement present in the system, a concept we define as purity-entanglement complementarity. Moreover, we demonstrate that in many pertinent scenarios, the optimal performance can be precisely determined through semidefinite programming techniques. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation. We demonstrate this by evaluating the amount of entanglement for a class of bound entangled states.

quant-ph↗

arXiv2023

Coherence manipulation in asymmetry and thermodynamics

In the classical regime, thermodynamic state transformations are governed by the free energy. This is also called as the second law of thermodynamics. Previous works showed that, access to a catalytic system allows us to restore the second law in the quantum regime when we ignore coherence. However, in the quantum regime, coherence and free energy are two independent resources. Therefore, coherence places additional non-trivial restrictions on the the state transformations, that remains elusive. In order to close this gap, we isolate and study the nature of coherence, i.e., we assume access to a source of free energy. We show that allowing catalysis along with a source of free energy allows us to amplify any quantum coherence present in the quantum state arbitrarily. Additionally, any correlations between the system and the catalyst can be suppressed arbitrarily. Therefore, our results provide a key step in formulating a fully general law of quantum thermodynamics.

quant-ph↗

arXiv2023

Catalytic and asymptotic equivalence for quantum entanglement

Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.

quant-ph↗

arXiv2023

Quantitative non-classicality of mediated interactions

In plethora of physical situations one can distinguish a mediator -- a system that couples other, non-interacting systems. Often the mediator itself is not directly accessible to experimentation, yet it is interesting and sometimes crucial to understand if it admits non-classical properties. An example of this sort that recently enjoys considerable attention are two quantum masses coupled via gravitational field. It has been argued that the gain of quantum entanglement between the masses indicates non-classicality of the states of the whole tripartite system. Here, we focus on non-classical properties of the involved interactions rather than the states. We derive inequalities whose violation indicates non-commutativity and non-decomposability (open system generalisation of non-commuting unitaries) of interactions through the mediators. The derivations are based on properties of general quantum formalism and make minimalistic assumptions about the studied systems, in particular the interactions can remain uncharacterised throughout the assessment. Furthermore, we also present conditions that solely use correlations between the coupled systems, excluding the need to measure the mediator. Next, we show that the amount of violation places a lower bound on suitably defined degree of non-decomposability. This makes the methods quantitative and at the same time experiment ready. We give applications of these techniques in two different fields: for detecting non-classicality of gravitational interaction and in bounding the Trotter error in quantum simulations.

quant-ph↗

arXiv2023

Generalised Uncertainty Relations from Finite-Accuracy Measurements

In this short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived within the context of canonical quantum theory, without the need for modified commutation relations. A GUP-type relation naturally emerges when the standard position operator is replaced by an appropriate Positive Operator Valued Measure (POVM), representing a finite-accuracy measurement that localises the quantum wave packet to within a spatial region $σ_g > 0$. This length scale is the standard deviation of the envelope function, $g$, that defines the POVM elements. Similarly, an EUP-type relation emerges when the standard momentum operator is replaced by a POVM that localises the wave packet to within a region $\tildeσ_g > 0$ in momentum space. The usual GUP and EUP are recovered by setting $σ_g \simeq \sqrt{\hbar G/c^3}$, the Planck length, and $\tildeσ_g \simeq \hbar\sqrt{Λ/3}$, where $Λ$ is the cosmological constant. Crucially, the canonical Hamiltonian and commutation relations, and, hence, the canonical Schr{\" o}dinger and Heisenberg equations, remain unchanged. This demonstrates that GUP and EUP phenomenology can be obtained without modified commutators, which are known to lead to various pathologies, including violation of the equivalence principle, violation of Lorentz invariance in the relativistic limit, the reference frame-dependence of the `minimum' length, and the so-called soccer ball problem for multi-particle states.

gr-qc↗

arXiv2022

Is there a finite complete set of monotones in any quantum resource theory?

Entanglement quantification aims to assess the value of quantum states for quantum information processing tasks. A closely related problem is state convertibility, asking whether two remote parties can convert a shared quantum state into another one without exchanging quantum particles. Here, we explore this connection for quantum entanglement and for general quantum resource theories. For any quantum resource theory which contains resource-free pure states, we show that there does not exist a finite set of resource monotones which completely determines all state transformations. We discuss how these limitations can be surpassed, if discontinuous or infinite sets of monotones are considered, or by using quantum catalysis. We also discuss the structure of theories which are described by a single resource monotone and show equivalence with totally ordered resource theories. These are theories where a free transformation exists for any pair of quantum states. We show that totally ordered theories allow for free transformations between all pure states. For single-qubit systems, we provide a full characterization of state transformations for any totally ordered resource theory.

quant-ph↗

arXiv2022

Hierarchy of correlation quantifiers comparable to negativity

Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different sets of states. However, these quantifiers are usually hard to compute as their definition involves optimization aiming to find the closest states within the set. On the other hand, negativity is one of the few computable entanglement monotones, but its comparison with other correlations required further justification. Here we place negativity as part of a family of correlation measures that has a distance-based construction. We introduce a suitable distance, discuss the emerging measures and their applications, and compare them to relative entropy-based correlation quantifiers. This work is a step towards correlation measures that are simultaneously comparable and computable.

quant-ph↗

arXiv2021

Cooperation and dependencies in multipartite systems

We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations.

quant-ph↗

arXiv2018

Detecting non-decomposability of time evolution via extreme gain of correlations

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.

quant-ph↗

arXiv2018

Entanglement gain in measurements with unknown results

We characterise non-selective global projective measurements capable of increasing quantum entanglement between two particles. We show that non-selective global projective measurements are capable of increasing entanglement between two particles, in particular, entanglement of any pure non-maximally entangled state can be improved in this way (but not of any mixed state) and we provide detailed analysis for two qubits. It is then shown that Markovian open system dynamics can only approximate such measurements, but this approximation converges exponentially fast as illustrated using Araki-Zurek model. We conclude with numerical evidence that macroscopic bodies in a random pure state do not gain entanglement in a random non-selective global measurement.

quant-ph↗