arXiv subjects

Borivoje Dakić

Publications and source records attributed to Borivoje Dakić.

At least 37 records · Page 2Linked to original sources

arXiv2023

Accessing inaccessible information via quantum indistinguishability

In this paper we present and analyze an information-theoretic task that consists in learning a bit of information by spatially moving the "target" particle that encodes it. We show that, on one hand, the task can be solved with the use of additional independently prepared quantum particles, only if these are indistinguishable from the target particle. On the other hand, the task can be solved with the use of distinguishable quantum particles, only if they are entangled with the target particle. Our task thus provides a new example in which the entanglement apparently inherent to independently prepared indistinguishable quantum particles is put into use for information processing. Importantly, a novelty of our protocol lies in that it does not require any spatial overlap between the involved particles. Besides analyzing the class of quantum-mechanical protocols that solve our task, we gesture towards possible ways of generalizing our results and of applying them in cryptography.

quant-ph↗

arXiv2023

On The Stabilizer Formalism And Its Generalization

The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem. This work analyzes the mathematical structure behind this theorem to find possible generalizations and derivation of constraints required for constructing a non-trivial generalized Clifford group. We prove that if the closure of the stabilizing set is dense in the set of $SU(d)$ transformations, then the associated Clifford group is trivial, consisting only of local gates and permutations of subsystems. This result demonstrates the close relationship between the density of the stabilizing set and the simplicity of the corresponding Clifford group. We apply the analysis to investigate stabilization with binary observables for qubits and find that the formalism is equivalent to the standard stabilization for a low number of qubits. Based on the observed patterns, we conjecture that a large class of generalized stabilizer states are equivalent to the standard ones. Our results can be used to construct novel Gottesman-Knill-type results and consequently draw a sharper line between quantum and classical computation.

quant-ph↗

arXiv2022

Dissipative phase transitions in optomechanical systems

We show that optomechanical quantum systems can undergo dissipative phase transitions within the limit of small nonlinear interaction and strong external drive. In such a defined thermodynamical limit, the nonlinear interaction stabilizes optomechanical dynamics in strong and ultrastrong coupling regimes. As a consequence optomechanical systems possess a rich phase diagram consisting of periodic orbits, discontinuous, and continuous dissipative phase transitions with and without bifurcation. We also find a critical point where continuous and discontinuous dissipative phase transition lines meet. Our analysis demonstrates that optomechanical systems are valuable for understanding the rich physics of dissipative phase transitions and ultrastrong coupling regimes.

quant-ph↗

arXiv2022

The Axiom of Choice and the No-Signaling Principle

We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known that probabilistic no-signaling resources (such as quantum non-locality) are stronger than deterministic ones, we show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones. To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signaling with respect to any probabilistic no-signaling resource.

quant-ph↗

arXiv2022

Quantum verification and estimation with few copies

As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges in the employment of such systems for reliable quantum information processing. Though the most complete technique is undoubtedly full tomography, the inherent exponential increase of experimental and post-processing resources with system size makes this approach infeasible even at moderate scales. For this reason, there is currently an urgent need to develop novel methods that surpass these limitations. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity), and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography, which enables the estimation of arbitrary elements of an unknown state with a number of copies that is low and independent of the system's size. These hyper-efficient techniques define a dimensional demarcation for partial tomography and open a path for novel applications.

quant-ph↗

arXiv2022

Universal quantum computation via quantum controlled classical operations

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of $2n$ target bits together with a set of classical gates controlled by log$(2n+1)$ ancillary qubits. We show that this model is equivalent to a quantum computer operating on $n$ qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.

quant-ph↗

arXiv2022

Sample-efficient device-independent quantum state verification and certification

Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years. When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce. Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource. Such strong assumptions deprive the verification procedure of its truly device-independent character. In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. Remarkably, we show that device-independent verification can be performed with optimal sample efficiency. Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.

quant-ph↗

arXiv2021

Experimental Higher-Order Interference in a Nonlinear Triple Slit

Interference between two waves is a well-known concept in physics, and its generalization to more than two waves is straight-forward. The order of interference is defined as the number of paths that interfere in a manner that cannot be reduced to patterns of a lower order. In practice, second-order interference means that in, say, a triple-slit experiment, the interference pattern when all three slits are open can be predicted from the interference patterns between all possible pairs of slits. Quantum mechanics is often said to only exhibit second-order interference. However, this is only true under specific assumptions, typically single-particles undergoing linear evolution. Here we experimentally show that nonlinear evolution can in fact lead to higher-order interference. The higher-order interference in our experiment has a simple quantum mechanical description; namely, optical coherent states interacting in a nonlinear medium. Our work shows that nonlinear evolution could open a loophole for experiments attempting to verify Born's rule by ruling out higher-order interference.

quant-ph↗

arXiv2021

Macroscopically nonlocal quantum correlations

It is usually believed that coarse-graining of quantum correlations leads to classical correlations in the macroscopic limit. Such a principle, known as macroscopic locality, has been proved for correlations arising from independent and identically distributed (IID) entangled pairs. In this letter we consider the generic (non-IID) scenario. We find that the Hilbert space structure of quantum theory can be preserved in the macroscopic limit. This leads directly to a Bell violation for coarse-grained collective measurements, thus breaking the principle of macroscopic locality.

quant-ph↗

arXiv2021

Higher-order interference between multiple quantum particles interacting nonlinearly

The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with single particles and more slits produce interference fringes reducible to a combination of double-slit patterns it is usually argued that quantum interference occurs between pairs of trajectories, compactly denoted as second-order interference. Here we show that quantum mechanics in fact allows for interference of arbitrarily high order. This occurs naturally when one considers multiple quantum objects interacting in the presence of a nonlinearity, both of which are required to observe higher-order interference. We make this clear by treating a generalised multi-slit interferometer using second-quantisation. We then present explicit experimentally-relevant examples both with photons interacting in nonlinear media and an interfering Bose-Einstein condensate with particle-particle interactions. These examples are all perfectly described by quantum theory, and yet exhibit higher-order interference based on multiple particles interacting nonlinearly.

quant-ph↗

arXiv2021

Quantum enhancement to information acquisition speed

The speed of the transmission of a physical signal from a sender to a receiver is limited by the speed of light, regardless of the physical system being classical or quantum. In this sense, quantum mechanics can not provide any enhancement of the speed of information. If instead we consider that the information needing to be transmitted is not localized at the sender's location, but dispersed throughout space, spatial coherence might provide an enhancement of the information speed. In this work, we demonstrate a quantum mechanical advantage in the speed of acquirement and transmission of information globally encoded in space. We present a task for which we prove a quadratic enhancement to the information speed of quantum information carriers with respect to their classical counterpart. Our findings can naturally be applied in situations where the information source has limited power, i.e. bounded number of signals that can be sent per unit time.

quant-ph↗

arXiv2021

Interference as an information-theoretic game

The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a broader class of processes, which can be formulated as information-processing tasks, providing a clear cut between classical, quantum and higher-order theories. The tasks involve two parties and communication between them with the goal of winning certain parity games. We show that the order of interference is in one-to-one correspondence with the parity order of these games. Furthermore, we prove the order of interference to be additive under composition of systems both in classical and quantum theory. The latter result can be used as a (semi)device-independent witness of the number of particles in the quantum setting. Finally, we extend our game formulation within the generalized probabilistic framework and prove that tomographic locality implies the additivity of the order of interference under composition. These results shed light on the operational meaning of the order of interference and can be important for the identification of the information-theoretic principles behind second-order interference in quantum theory.

quant-ph↗

arXiv2020

Fourier Transform of the Orbital Angular Momentum of a Single Photon

Optical networks implementing single-qudit quantum computation gates may exhibit superior properties to those for qubits as each of the optical elements in the network can work in parallel on many optical modes simultaneously. We present an important class of such networks, that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily large dimension. These networks redistribute the initial quantum state into the path and orbital angular momentum (OAM) degrees of freedom and exhibit two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly $O(d)$ with the dimension $d$ of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital angular momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with non-trivial phase profiles. In contrast, we present a different approach that utilizes only conventional optical elements.

quant-ph↗

arXiv2020

On the central limit theorem for unsharp quantum random variables

In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit distribution of relative frequency. We provide the de Finetti-type representation theorem for all separable states, showing that the distribution can be well approximated by mixture of normal distributions. No symmetry restrictions, such as the permutational invariance were needed. Furthermore, we investigate the convergence rates and show that the relative frequency can stabilize to some constant at best at the rate of order $1/\sqrt{N}$ for all separable inputs. On the other hand, we provide an example of a strictly unsharp quantum measurement where the better rates are achieved by using entangled inputs. This means that in certain cases the noise generated by the measurement process can be suppressed by using entanglement. We deliver our result in the form of quantum information task where the player achieves the goal with certainty in the limiting case by using entangled inputs or fails with certainty by using separable inputs.

quant-ph↗

arXiv2020

Bell's theorem for trajectories

In classical theory, the trajectory of a particle is entirely predetermined by the complete set of initial conditions via dynamical laws. Based on this, we formulate a no-go theorem for the dynamics of classical particles, i.e., a Bell's inequality for trajectories, and discuss its possible violation in a quantum scenario. A trajectory, however, is not an outcome of a quantum measurement, in the sense that there is no observable associated with it, and thus there is no "direct" experimental test of the Bell's inequality for trajectories. Nevertheless, we show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time. Such inequality is indeed violated by quantum mechanics, and the violation persists during an entire interval of time and not just at a particular singular instant. We interpret the violation to imply that trajectories (or at least pieces thereof) cannot exist predetermined, within a local-realistic theory.

quant-ph↗

arXiv2020

Selective Quantum State Tomography

We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be done with the following notable advantages (i) a number of state copies that depends only on the desired precision of the estimation, rather than the dimension of the unknown state; (ii) a similar reduction in the requisite classical memory and computational cost; (iii) an approach to state tomography using $O(ε^{-2}\log d)$ state copies for maximum norm error $ε$, as well as achieving nearly optimal bounds for full tomography with independent measurements. As an immediate extension to this technique we proceed to show that SQST can be used to generate an universal data sample, of fixed and dimension independent size, from which one can extract the mean values from a continuous class of operators on demand.

quant-ph↗

arXiv2020

Coherence Equality and Communication in a Quantum Superposition

In this paper, we introduce a "coherence equality" that is satisfied by any classical communication -- i.e., conveyed by a localized carrier traveling along well defined directions. In contrast, this equality is violated when the carrier is prepared in a quantum superposition of communication directions. This is phrased in terms of the success probability of a certain communication task, which results to be always constant and equal to 1/2 in the classical case. On the other hand, we develop two simple quantum schemes that deviate systematically from the classical value, thus violating the coherence equality. Such a violation can also be exploited as an operational way to witness spatial quantum superpositions without requiring the use of an interferometer, but only by means of spatially separated local measurements.

quant-ph↗

arXiv2018

Experimental few-copy multi-particle entanglement detection

Quantum technologies lead to a variety of applications that outperform their classical counterparts. In order to build a quantum device it must be verified that it operates below some error threshold. Recently, because of technological developments which allow for the experimental realization of quantum states with increasing complexity, these tasks must be applied to large multi-qubit states. However, due to the exponentially-increasing system size, tasks like quantum entanglement verification become hard to carry out in such cases. Here we develop a generic framework to translate any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence to detect entanglement grows exponentially with the number of individual detection events. To benchmark our findings, we experimentally verify the presence of entanglement in a photonic six-qubit cluster state generated using three single-photon sources operating at telecommunication wavelengths. We find that its presence can be certified with at least 99.74% confidence by detecting 20 copies of the quantum state. Additionally, we show that genuine six-qubit entanglement is verified with at least 99% confidence by using 112 copies of the state. Our protocol can be carried out with a remarkably low number of copies, making it a practical and applicable method to verify large-scale quantum devices.

quant-ph↗