Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that interference is real and input components undergo energy redistribution. Both interpretations entail the same observable consequences at the macroscopic level, but the first approach is considerably more popular. This preference was established before the emergence of quantum mechanics. Unfortunately, it requires a non-classical underlying mechanism and fails to explain well-known microscopic observations. Classical physics appears to collapse at the quantum level. On the other hand, quantum superposition can be described as a classical process if the second alternative is adopted. The gap between classical mechanics and quantum mechanics is an interpretive problem.
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
We propose a criterion which defines whether a superposition of two photonic components is macroscopic. It is based on the ability to discriminate these components with a particular class of "classical" detectors, namely a photon number measurement with a resolution coarse-grained by noise. We show how our criterion can be extended to a measure of the size of macroscopic superpositions by quantifying the amount of noise that can be tolerated and taking the distinctness of two Fock states differing by N photons as a reference. After applying our measure to several well-known examples, we demons…
For three given probability distributions describing positions of three classical coins the quantum density matrix of spin-$1/2$ state is constructed and its matrix elements are associated with triada of Malevich's squares. The superposition principle of spin-$1/2$ states is presented in the form of nonlinear addition rule for these classical coin probabilities. We illustrate the formulas by the statement"God does not play dice - God plays coins".
In the Hilbert space formulation of classical mechanics (CM), pioneered by Koopman and von Neumann (KvN), there are potentially more observables that in the standard approach to CM. In this paper we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the KvN is extended to include the evolution of differential forms. Because of their non-invariance, those extra observables have to be removed. This removal makes the superposition of states in KvN, and as a consequence also in CM, impossible.
We describe a set of measurement protocols for performing non-classicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this methods for detecting non-classical mechanical states. We then show that the generalization of this techniques to multiple resonator modes allows the conditioned preparation and the det…
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superpositi…
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) generated by a quantum injected optical parametric amplifier (QI-OPA) and involving a number of photons in excess of 5x10^4 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on coherent states and NOON states, in the perspective of the comprehensive theory of the subject by W.H.Zurek. In that perspective the concepts of "pointer state", "einselection" are applied to the new scheme.
Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here we show that the ability to place N completely depolarising channels in a superposition of N alternative causal orders enables a high-fidelity, heralded transmission of…
Error correction will add so much overhead to large quantum computations that we suspect the most efficient algorithms will use a classical co-processor to do as much work as possible. We present a method to offload portions of a quantum computation to a classical computer by producing a superposition of masks which hide a quantum input. With the masks, we can measure the result without altering the original input and then perform classical computations on the measured output. If the task has enough structure, the classical computations will be equivalent to a quantum computation performed in …
Quantum entanglement is the quintessence of quantum information processing mostly limited to the microscopic regime governed by Heisenberg uncertainty principle. For practical applications, however, macroscopic entanglement gives great benefits in both photon loss and sensitivity. Recently, a novel method of macroscopic entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where superposition between binary bases in each interferometric system plays a key role. Here, the function of path superposition applied to independent …
Simulating quantum measurements without superposition devices
Lund University（隆德大学）；Instituto de física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Uppsala University（乌普萨拉大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
Nonlinear coherent states (CSs) and their {\it dual families} were introduced recently. In this paper we want to obtain their superposition and investigate their non-classical properties such as antibunching effect, quadrature squeezing and amplitude squared squeezing. For this purpose two types of superposition are considered. In the first type we neglect the normalization factors of the two components of the dual pair, superpose them and then we normalize the obtained states, while in the second type we superpose the two normalized components and then again normalize the resultant states. As…
Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible between quantum evolutions. We characterize such superpositions here. A resource theoretic framework is developed to quantify superposition present in an arbitrary quantum evolution. In addition to characterization, the framework considers superposition as a quantum resource. This resource can be exploited to perform certain quantum tasks that are otherwise imposs…
Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking (effective hiding), as a special case of the corresponding general formalism (Bernstein). Critical values of the order parameters for this transition are determined by Heisenberg's indeterminacy relations, change continuously, and are in excellent agreement with the recent and remarkable experiments with Bose condensation. It is also shown that such a phase…
As it is known, neither classical logical conjunction "and" nor classical logical alternative "either...or" can replace "+" representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In the paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this appro…
Here we discuss generation of non-classical states of bosonic mode with the help of artificially designed loss, namely the nonlinear coherent loss. We show how to generate superpositions of Fock states, and how it is possible to "comb" the initial states leaving only states with certain properties in the resulting superposition (for example, a generation of a superposition of Fock states with odd number of particles). We discuss purity of generated states and estimate maximal achievable generation fidelity.
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 coh…
Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that, under ideal conditions, the evolution of the system would be unitary, generated by an effective Hamiltonian. We describe also an incoherent use of the device that achieves the same effective evolution on an ensemble. The effective Hamiltonian thus generated may have qualitatively different features from that associated to a classical value of the parameter.
The ability to generate light in a pure quantum state is essential for advances in optical quantum technologies. However, obtaining quantum states with control in the photon-number has remained elusive. Optical light fields with zero and one photon can be produced by single atoms, but so far it has been limited to generating incoherent mixtures, or coherent superpositions with a very small one-photon term. Here, we report on the on-demand generation of quantum superpositions of zero, one, and even two photons, via pulsed coherent control of a single artificial atom. Driving the system up to fu…
The constraints arising for a general set of causal relations, both classically and quantumly, are still poorly understood. As a step in exploring this question, we consider a coherently controlled superposition of "direct-cause" and "common-cause" relationships between two events. We propose an implementation involving the spatial superposition of a mass and general relativistic time dilation. Finally, we develop a computationally efficient method to distinguish such genuinely quantum causal structures from classical (incoherent) mixtures of causal structures and show how to design experiment…
In this work, we study the transmission of classical information through three completely depolarizing channels in superposition of different causal orders. We thus introduce the quantum 3-switch as a resource for quantum communications. We perform a new kind of quantum control that was not accessible to the previously treated two-channel case. The fine and full quantum control achieved using selected combinations of causal orders let us uncover new features: non monotonous behavior on the transmission of information with respect to the number of causal orders involved, and different values of…
We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such a…
If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with $N$ depolarizing channels put in superposition of $M$ causal orders via quantum SWITCH. We calculate Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with $M$ and it is independent of $N$. For a qubit it never reaches $1$ if we are increasing $M$. On the other hand, the classical capacity decreases wit…
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We pr…
We propose a modified dynamics of quantum mechanics, in which classical mechanics of a point mass derives intrinsically in a massive limit of a single-particle model. On the premise that a position basis plays a special role in wavefunction collapse, we deduce to formalize spontaneous localization of wavefunction on the analogy drawn from thermodynamics, in which a characteristic energy scale and a time scale are introduced to separate quantum and classical regimes.
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. The former universally achieves corner points of the capacity region and the latter u…
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by wha…
Gong points out [quant-ph arXiv:1106.0062] a "direct connection" between our measure [PRL 106, 220401 (2011)] recently proposed to quantify macroscopic quantum superpositions and a previously studied quantity introduced to study classical and quantum chaos. We point out that the two measures are obviously different for some mixed states, and the previous one does not work as a sensible measure to quantify quantum superpositions.
In this paper we analyze the definition of quantum superpositions within orthodox Quantum Mechanics (QM) and their relation to physical reality. We will begin by discussing how the metaphysical presuppositions imposed by Bohr on the interpretation of QM have become not only interpretational dogmas which constrain the limits of the present Orthodox Line of Research (OLR), but also how these desiderata implicitly preclude the possibility of developing a physical representation of quantum superpositions. We will then continue analyzing how most interpretations of QM argue against the existence of…
The largest ensemble of qubits which satisfy the general transformation of equal superposition is obtained by different methods, namely, linearity, no-superluminal signalling and non-increase of entanglement under LOCC. We also consider the associated quantum random walk and show that all unitary balanced coins give the same asymmetric spatial probability distribution. It is further illustrated that unbalanced coins, upon appropriate superposition, lead to new unbiased walks which have no classical analogues.
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the density matrices induced by the experim…
In the classical world, temperature is a measure of how hot or cold a physical object is. We never find a physical system which can be both hot and cold at the same time. Here, we show that for a quantum system, it is possible to have superposition of two temperatures which can lead to a situation that it can be found both in hot and cold state. We propose a physical mechanism for how to create a quantum state which is superposition of two temperatures. Furthermore, we define an operator for the inverse temperature and show that the thermal state is, in fact, an eigenstate of this operator. Th…
We describe how quasiclassical relative positions of particles emerge in an initially delocalized quantum system as scattering of a probe beam is observed. We show that in the multiparticle case this localization in position space occurs via intermediate states that are quantum superpositions of spatial configurations. These superpositions are robust to consecutive scattering events, and scattering alone does not lead to their decoherence. Instead the free evolution of the system combines with scattering to destroy these superpositions, leading the particles to adopt classical-like positions r…
We propose a robust scheme for generating macroscopic superposition states of spin or motion with the aid of a single photon. Shaping the wave packet of the photon enables high-fidelity preparation of non-classical states of matter even in the presence of photon loss. Success is heralded by photodetection, enabling the scheme to be implemented with a weak coherent field. We analyze applications to preparing Schrödinger cat states of a collective atomic spin or of a mechanical oscillator coupled to an optical resonator. The method generalizes to preparing arbitrary superpositions of coherent st…
Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by 'superposition' in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid 'contradiction'. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, as a key element of the formal structure of the t…
We study a coherent superposition of field annihilation and creation operator acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.
We present the experimental realization of a scheme, based on single-photon interference, for implementing superpositions of distinct quantum operations. Its application to a thermal light field (a well-categorized classical entity) illustrates quantum superposition from a new standpoint and provides a direct and quantitative verification of the bosonic commutation relation between creation and annihilation operators. By shifting the focus towards operator superpositions, this result opens interesting alternative perspectives for manipulating quantum states.
It is of folkloric belief that the security of classical cryptographic protocols is automatically broken if the Adversary is allowed to perform superposition queries and the honest players forced to perform actions coherently on quantum states. Another widely held intuition is that enforcing measurements on the exchanged messages is enough to protect protocols from these attacks. However, the reality is much more complex. Security models dealing with superposition attacks only consider unconditional security. Conversely, security models considering computational security assume that all suppos…
Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to demonstrate that quantum physics deviates from classical causality in the limit of small action. Here, I point out that this proof constitutes a failure of the principle of least action and consider possible implications for our understanding of fundamental physics.
Quantum resources,such as discord and entanglement, are crucial in quantum information processing. In this paper, quantum resources are studied from the aspect of quantum state superposition. We define the local superposition (LS) as the superposition between basis of single part, and nonlocal superposition (NLS) as the superposition between product basis of multiple parts. For quantum resource with nonzero LS, quantum operation must be introduced to prepare it, and for quantum resource with nonzero NLS, nonlocal quantum operation must be introduced to prepare it. We prove that LS vanishes if …
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it has recently been theoretically predicted that superimposing quantum circuits, each with a different gate order, could provide quantum computers with an even further computational advantage [3-5]. Here, we experimentally demonstrate this enhancement by applying two quantum gates in a superposition of both possible orders to determine whether the two gates comm…
Reflection of a microscopic particle from a mesoscopic/macroscopic `mirror' generates two-body correlated interference from the incident and reflected particle substates and their associated mirror substates. The microscopic momentum exchanged generates two mirror substates which interfere to produce fringes which do not vanish as the mirror mass increases. The small displacement between these mirror states can yield negligible environmental decoherence times. Mirror coherence lengths impose constraints on the extent of this interference, which are mitigated using interference of the two-body …
We present a simple protocol to purify a coherent-state superposition that has undergone a linear lossy channel. The scheme constitutes only a single beam splitter and a homodyne detector, and thus is experimentally feasible. In practice, a superposition of coherent states is transformed into a classical mixture of coherent states by linear loss, which is usually the dominant decoherence mechanism in optical systems. We also address the possibility of producing a larger amplitude superposition state from decohered states, and show that in most cases the decoherence of the states are amplified …
Can it possibly be that the proper interpretation of quantum theory, which allows a quantum system to be in a superposition of mutually exclusive states, is itself a superposition of seemingly contradicting interpretations?
Quantum superposition is the heart of quantum mechanics as mentioned by Dirac and Feynman. In an interferometric system, single photon self-interference has been intensively studied over the last several decades in both quantum and classical regimes. In Born rule tests, the Sorkin parameter indicates the maximum number of possible quantum superposition allowed to the input photons entering an interferometer, where multi-photon interference fringe is equivalent to that of a classical version by a laser. Here, an attenuated laser light in a quantum regime is investigated for self-interference in…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is…
In this research, we present a quantum circuit design and implementation for a parallel universal linear bounded automata. This circuit is able to accelerate the inference of algorithmic structures in data for discovering causal generative models. The computation model is practically restricted in time and space resources. A classical exhaustive enumeration of all possible programs on the automata is shown for a couple of example cases. The precise quantum circuit design that allows executing a superposition of programs, along with a superposition of inputs as in the standard quantum Turing ma…
We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ($\hat{a}$) and creation ($\hat{a}^†$) operators of the type ($s \hat{a}\hat{a}^†+ t \hat{a}^†\hat{a}$), with $s^2 + t^2 = 1$. Such an operation, when applied on states with classical features, is shown to introduce strong nonclassicality. We quantify the generated degree of nonclassicality by the negative volume of Wigner distribution in the phase space and investigate two other observable nonclassical features, sub-Poissonian statistics and squeezing…
We report the successful generation of an entangled multiparticle quantum superposition of pure photon states. They result from a multiple (universal} cloning of a single photon qubit by a high gain, quantum-injected parametric amplifier. The information preserving property of the process suggests for these states the name of ''multi-particle qubits''. They are ideal objects for investigating the emergence of the classical world in quantum systems with increasing complexity, the decoherence processes and may allow the practical implementation of the universal 2-qubit logic gates.
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schroedinger dynamics and irreversible processes of diffusion. Moreover, said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical "decay of the wave packet" is shown to simply r…
