## Journals

### Note on Bose-Einstein condensation of photons. (arXiv:1801.05220v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

This paper provides, firstly, a succinct mathematical derivation of Bose-Einstein condensation (BEC) of photons elaborating on previous results [M\"uller, E.E., Annals of Phys. 184, 219-230 (1988); M\"uller, E.E. Physica 139A, 165-174 (1986)] including new results on the condensate function, and, secondly, applies this framework to consistently explain experimental findings reported in Klaers J., Schmitt, J., Vewinger, F & Weitz, M., Nature 468, 545-548 (2010). The theoretical approach presented here invites to significantly widen the experimental framework for BEC of photons including three-dimensional photon resonators and thermalization mechanisms different from a dye medium in the cavity.

Categories: Journals, Physics

### Accurate density measurement of a cold Rydberg gas via non collisional two-body transitions. (arXiv:1801.05228v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We experimentally demonstrate an original method to measure very accurately the density of a frozen Rydberg gas. It is based on the use of adiabatic transitions induced by the long-range dipole-dipole interaction in pairs of nearest neighbor Rydberg atoms by sweeping an electric field with time. The efficiency of this two-body process is experimentally tunable, depends strongly on the density of the gas and can be accurately calculated. The analysis of this efficiency leads to an accurate determination of the Rydberg gas density, and to a calibration of the Rydberg detection. Our method does not require any prior knowledge or estimation of the volume occupied by the Rydberg gas, or of the efficiency of the detection.

Categories: Journals, Physics

### Various complexity measures in confined hydrogen atom. (arXiv:1801.05232v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these quantities with R\'enyi entropy ($R$) is explored here. The role of scaling parameter in the exponential part is also pursued. $R$ is evaluated taking order of entropic moments $\alpha, \beta$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces. Detailed systematic results of these measures with respect to variation of confinement radius $r_c$ is presented for low-lying states such as, $1s$-$3d,~4f$ and $5g$. For \emph{nodal} states, such as $2s,~3s$ and $3p$, as $r_c$ progresses there appears a maximum followed by a minimum in $r$ space, having certain values of the scaling parameter. However, the corresponding $p$-space results lack such distinct patterns. This study reveals many other interesting features.

Categories: Journals, Physics

### Information is not a thermodynamic resource. (arXiv:1801.05237v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

The so-called information-thermodynamics link has been created in a series of works starting from Maxwell demon and established by the idea of transforming information into work in the though experiment of Szilard which then evolved into the vast field of research. The aim of this note is firstly to present two new models of the Szilard engine containing arbitrary number of molecules which show irrelevance of acquiring information for work extraction. Secondly, the difference between the definition of entropy for ergodic systems and systems with ergodicity breaking constraints is emphasized. The role of nonergodic systems as information carriers and the thermodynamic cost of stability and accuracy of information encoding and processing is briefly discussed.

Categories: Journals, Physics

### de Finetti reductions for partially exchangeable probability distributions. (arXiv:1801.05240v1 [math.PR])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability, and some generalizations of these. Our techniques are combinatorial and rely on the "BEST" theorem, enumerating the Eulerian cycles of a multigraph.

Categories: Journals, Physics

### Deterministic teleportation of a quantum gate between two logical qubits. (arXiv:1801.05283v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum systems. One approach to this challenge is to utilize modularity--a pervasive strategy found throughout nature and engineering--to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations motivate the development of a quantum modular architecture, where separate quantum systems are combined via communication channels into a quantum network. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate, a technique originally proposed in 1999 which, until now, has not been realized deterministically. Here, we experimentally demonstrate a teleported controlled-NOT (CNOT) operation made deterministic by utilizing real-time adaptive control. Additionally, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between logical qubits, encoding quantum information redundantly in the states of superconducting cavities. Such teleported operations have significant implications for fault-tolerant quantum computation, and when realized within a network can have broad applications in quantum communication, metrology, and simulations. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits within an error-protected quantum modular architecture.

Categories: Journals, Physics

### On the possibility of a realist ontological commitment in quantum mechanics. (arXiv:1801.05307v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.

Categories: Journals, Physics

### Quantum mechanics allows undetectable inconsistencies in witnessed events. (arXiv:1801.05317v1 [physics.gen-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an experimenter to determine which measurement bases have been used by another experimenter. As a consequence, quantum mechanics allows a situation in which two experimenters witness incoherent stories without being able to detect such incoherence, even if they are allowed to communicate freely by exchanging iterative and bilateral messages.

Categories: Journals, Physics

### Relativistic Lippmann - Schwinger equation. (arXiv:1801.05370v1 [math-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

The classical Lippmann-Schwinger equation plays an important role in the scattering theory (non-relativistic case, Schr\"odinger equation). In the present paper we consider the relativistic analogue of the Lippmann-Schwinger equation. We represent the corresponding equation in the integral form. Using this integral equation we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.

Categories: Journals, Physics

### Time from quantum state complexity and the pace of time flow. (arXiv:1801.05379v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

Based on the hypothesis that the thermodynamic arrow of time is an emergent phenomenon of quantum state complexity evolution, we further propose that the natural pace of time flow is proportional to the changing rate of quantum state complexity. we then testify how the pace of time flow changes under both special and general relativity based on the analogy between qubit quantum operations and Lorentz transformations. Our simulation results show a qualitative consistency between our hypothesis and the time dilation effect of relativity. We also checked the relationship between our idea on time with the thermal time hypothesis and we showed that our idea can be regarded as a natural generalization of the thermal time hypothesis.

Categories: Journals, Physics

### Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops. (arXiv:1801.05390v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal correlations present in a tensor network is proposed, which quantifies the extent of resonances around closed loops in the network. Finally we describe an algorithm for the optimal truncation of an internal index from a tensor network, based upon proper removal of the redundant internal correlations. These results, which offer a unified theoretical framework for the manipulation of tensor networks with closed loops, can be applied to improve existing tensor network methods for the study of many-body systems and may also constitute key algorithmic components of sophisticated new tensor methods.

Categories: Journals, Physics

### Harmonic oscillator in an elastic medium with a spiral dislocation. (arXiv:1801.05404v1 [quant-ph])

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schr\"odinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.

Categories: Journals, Physics

### Quantum Mechanics in symmetry language. (arXiv:1305.4349v6 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.

Categories: Journals, Physics

### Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices. (arXiv:1612.03363v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies. They quantify the randomness of the successive quantum measurement results in the case where the evolution of the system between each two consecutive measurements is described by a given unitary operator. We study the class of chaotic unitaries, i.e., the ones of maximal entropy or, equivalently, such that they can be represented by suitably rescaled complex Hadamard matrices in some orthonormal bases. We provide necessary conditions for a unitary operator to be chaotic, which become also sufficient for qubits and qutrits. These conditions are expressed in terms of the relation between the trace and the determinant of the operator. We also compute the volume of the set of chaotic unitaries in dimensions two and three, and the average PVM-dynamical entropy over the unitary group in dimension two. We prove that this mean value behaves as the logarithm of the dimension of the Hilbert space, which implies that the probability that the dynamical entropy of a unitary is almost as large as possible approaches unity as the dimension tends to infinity.

Categories: Journals, Physics

### Pure states of maximum uncertainty with respect to a given POVM. (arXiv:1701.01139v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how 'badly' can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

Categories: Journals, Physics

### Diffraction-limited plenoptic imaging with correlated light. (arXiv:1703.03830v3 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

Traditional optical imaging faces an unavoidable trade-off between resolution and depth of field (DOF). To increase resolution, high numerical apertures (NA) are needed, but the associated large angular uncertainty results in a limited range of depths that can be put in sharp focus. Plenoptic imaging was introduced a few years ago to remedy this trade off. To this aim, plenoptic imaging reconstructs the path of light rays from the lens to the sensor. However, the improvement offered by standard plenoptic imaging is practical and not fundamental: the increased DOF leads to a proportional reduction of the resolution well above the diffraction limit imposed by the lens NA. In this paper, we demonstrate that correlation measurements enable pushing plenoptic imaging to its fundamental limits of both resolution and DOF. Namely, we demonstrate to maintain the imaging resolution at the diffraction limit while increasing the depth of field by a factor of 7. Our results represent the theoretical and experimental basis for the effective development of the promising applications of plenoptic imaging.

Categories: Journals, Physics

### Measurement of complete and continuous Wigner functions for discrete atomic systems. (arXiv:1706.08676v4 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing continuous Wigner functions for qubit or spin systems. We find that the Wigner function of all pure states of a qubit has negative regions and the negativity completely vanishes when the purity of an arbitrary mixed state is less than $\frac{2}{3}$. We experimentally demonstrate these findings using a single cesium atom confined in an optical dipole trap, which undergoes a nearly pure dephasing process. Our method can be applied straightforwardly to multi-atom systems for measuring the Wigner function of their collective spin state.

Categories: Journals, Physics

### Quantum Work in the Bohmian framework. (arXiv:1707.06159v3 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterised by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterisation of the dynamics of quantum systems, including the measurement process.

Categories: Journals, Physics

### The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting. (arXiv:1507.07341v5 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

The interaction of competing agents is described by the classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein-Podolsky-Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

Categories: Journals, Physics

### Max- relative entropy of coherence: an operational coherence measure. (arXiv:1707.08795v2 [quant-ph] UPDATED)

arXiv.org: Quantum Physics - Wed, 2018-01-17 04:45

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the max-relative entropy of coherence. By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit. Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.

Categories: Journals, Physics