arXiv subjects

Caslav Brukner

Publications and source records attributed to Caslav Brukner.

At least 37 records · Page 2Linked to original sources

arXiv2013

Quantum discord as resource for remote state preparation

Quantum entanglement is widely recognized as one of the key resources for the advantages of quantum information processing, including universal quantum computation, reduction of communication complexity or secret key distribution. However, computational models have been discovered, which consume very little or no entanglement and still can efficiently solve certain problems thought to be classically intractable. The existence of these models suggests that separable or weakly entangled states could be extremely useful tools for quantum information processing as they are much easier to prepare and control even in dissipative environments. It has been proposed that a requirement for useful quantum states is the generation of so-called quantum discord, a measure of non-classical correlations that includes entanglement as a subset. Although a link between quantum discord and few quantum information tasks has been studied, its role in computation speed-up is still open and its operational interpretation remains restricted to only few somewhat contrived situations. Here we show that quantum discord is the optimal resource for the remote quantum state preparation, a variant of the quantum teleportation protocol. Using photonic quantum systems, we explicitly show that the geometric measure of quantum discord is related to the fidelity of this task, which provides an operational meaning. Moreover, we demonstrate that separable states with non-zero quantum discord can outperform entangled states. Therefore, the role of quantum discord might provide fundamental insights for resource-efficient quantum information processing.

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arXiv2013

The classical limit of a physical theory and the dimensionality of space

In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own dimension- the minimal number of real parameters (coordinates) needed to specify the state of system or a point within the physical space. Within an operational framework to a physical theory, the two dimensions coincide in a natural way under the following "closeness" requirement: the dynamics of a single elementary system can be generated by the invariant interaction between the system and the "macroscopic transformation device" that itself is described from within the theory in the macroscopic (classical) limit. Quantum mechanics fulfils this requirement since an arbitrary unitary transformation of an elementary system (spin-1/2 or qubit) can be generated by the pairwise invariant interaction between the spin and the constituents of a large coherent state ("classical magnetic field"). Both the spin state space and the "classical field" are then embedded in the Euclidean three-dimensional space. Can we have a general probabilistic theory, other than quantum theory, in which the elementary system ("generalized spin") and the "classical fields" generating its dynamics are embedded in a higher-dimensional physical space? We show that as long as the interaction is pairwise, this is impossible, and quantum mechanics and the three-dimensional space remain the only solution. However, having multi-particle interactions and a generalized notion of "classical field" may open up such a possibility.

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arXiv2013

Condition for macroscopic realism beyond the Leggett-Garg inequalities

In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this paper, we discuss another necessary condition called no-signaling in time. It solely bases on comparing the probability distribution for a macrovariable at some time for the cases where previously a measurement has or has not been performed. Although the concept is analogous to the no-signaling condition in the case of Bell tests, it can be violated according to quantum mechanical predictions even in situations where no violation of Leggett-Garg inequalities is possible.

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arXiv2013

Bound entanglement helps to reduce communication complexity

We present a simple communication complexity problem where three parties benefit from sharing bound entanglement. This demonstrates that entanglement distillability of the shared state is not necessary in order to surpass classical communication complexity.

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arXiv2013

Quantum correlations with no causal order

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations which does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.

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arXiv2012

General relativistic effects in quantum interference of photons

Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon travelling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.

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arXiv2012

Probing Planck-scale physics with quantum optics

One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of experimental evidence of quantum gravitational effects thus far is a major hindrance. Yet, the quantization of space-time itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme that allows an experimental test of this conjecture by probing directly the canonical commutation relation of the center of mass mode of a massive mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for tabletop experiments to test possible quantum gravitational phenomena.

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arXiv2011

Quantum interferometric visibility as a witness of general relativistic proper time

Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising due to an Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Here we propose a novel quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a "clock" - a particle with evolving internal degrees of freedom - that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity proper time flows at different rates in different regions of space-time. Therefore, due to quantum complementarity the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the "clock". Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.

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arXiv2010

Necessary and sufficient condition for non-zero quantum discord

Quantum discord characterizes "non-classicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of non-zero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.

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arXiv2010

Are there fundamental limits for observing quantum phenomena from within quantum theory?

Does there exist a limit for the applicability of quantum theory for objects of large mass or size, or objects whose states are of large complexity or dimension of the Hilbert space? The possible answers range from practical limitations due to decoherence within quantum theory to fundamental limits due to collapse models that modify quantum theory. Here, we suggest the viewpoint that there might be also fundamental limits without altering the quantum laws. We first demonstrate that for two quantum spins systems of a given spin length, no violation of local realism can be observed, if the measurements are sufficiently coarse-grained. Then we show that there exists a fundamental limit for the precision of measurements due to (i) the Heisenberg uncertainty relation which has to be applied to the measuring apparatus, (ii) relativistic causality, and (iii) the finiteness of resources in any laboratory including the whole universe. This suggests that there might exist a limit for the size of the systems (dimension of the Hilbert space) above which no violation of local realism can be seen anymore.

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arXiv2010

Entanglement between smeared field operators in the Klein-Gordon vacuum

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.

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arXiv2010

Theories of systems with limited information content

We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary measurements, i.e. a complete knowledge of future outcome in one measurement is at the expense of complete uncertainty in the others. This is characteristic feature of the theories and they can be ordered according to the number of mutually complementary measurements which is also shown to define their computational abilities. In the theories multipartite states may contain entanglement and tomography with local measurements is possible. The classification includes both classical and quantum theory and also generalized probabilistic theories with higher number of degrees of freedom, for which operational meaning is given. We also discuss thought experiments discriminating standard quantum theory from the generalizations.

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arXiv2010

Macroscopic realism and spatiotemporal continuity

Macroscopic realism, as introduced by Leggett and Garg, is the world view in which properties of macroscopic systems exist independent of and are not influenced by measurement. Motivated by classical physical laws such as Newtonian mechanics or Maxwell's electrodynamics, in this work we add the restrictive postulate that the observables of macroscopic objects are evolved continuously through space and time. Quantum theory violates both macroscopic realism and the continuity assumption. While decoherence or collapse models (e.g. due to a universal noise background or gravitational self energy) can restore macroscopic realism, we show that a continuous spatiotemporal description does not become possible in general. This shines new light on the question how the classical world arises out of the quantum realm.

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arXiv2010

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.

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arXiv2010

Entanglement and communication-reducing properties of noisy N-qubit states

We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -- not requiring their further modification via stochastic local operations and classical communication such as entanglement purification or distillation procedures. We identify novel families of multi-particle states which are entangled but nevertheless allow local realistic description of specific Bell experiments. For some of them, the "gap" between the critical values for entanglement and violation of Bell inequality remains finite even in the limit of infinitely many qubits.

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arXiv2009

Bell's experiment with intra- and inter-pair entanglement: Single-particle mode entanglement as a case study

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared, independent pairs. In particular, one can have probabilistic violation of Bell's inequalities in which a finite fraction of all the runs result in violation, even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is "decided" by a sequence of quantum (random) outcomes.

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arXiv2009

The speed of quantum and classical learning for performing the k-th root of NOT

We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machine in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the k-th root of NOT (NOT = logical negation), with k=2^m and m \in N. The reason for this speed-up is that classical machine requires memory of size log k=m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k.

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arXiv2009

Entanglement detection with bounded reference frames

Quantum experiments usually assume the existence of perfect, classical, reference frames, which allow for the specification of measurement settings (e.g. orientation of the Stern Gerlach magnet in spin measurements) with arbitrary precision. If the reference frames are "bounded" (i.e. quantum systems themselves, having a finite number of degrees of freedom), only limited precision can be attained. Using spin coherent states as bounded reference frames we have found their minimal size needed to violate local realism for entangled spin systems. For composite systems of spin-1/2 particles reference frames of very small size are sufficient for the violation; however, to see this violation for macroscopic entangled spins, the size of the reference frame must be at least quadratically larger than that of the spins. Unavailability of such reference frames gives a possible explanation for the non-observance of violation of local realism in everyday experience.

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