We analyse nonperturbatively signal transmission patterns in Green's functions of interacting quantum fields. Quantum field theory is re-formulated in terms of the nonlinear quantum-statistical response of the field. This formulation applies equally to interacting relativistic fields and nonrelativistic models. Of crucial importance is that all causality properties to be expected of a response formulation indeed hold. Being by construction equivalent to Schwinger's closed-time-loop formalism, this formulation is also shown to be related naturally to both Kubo's linear response and Glauber's macroscopic photodetection theories, being a unification of the two with generalisation to the nonlinear quantum-statistical response problem. In this paper we introduce response formulation of bosons; response reformulation of fermions will be subject of a separate paper.
Phase-space techniques are generalized to nonlinear quantum electrodynamics beyond the rotating wave approximation, resulting in an essentially classical picture of radiation dynamics.
Wick's theorem in the Schwinger-Perel-Keldysh closed-time-loop formalism is written in a form where the place of contractions is taken by the linear response function of the field. This result demonstrates that the physical information supplied by Wick's theorem for operators is propagation of the free field in space and time.
It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system. The results are extended to non-interacting bosonic fields, both neutral and charged.
Generalised phase-space techniques for electromagnetic interactions beyond the rotating wave approximation [L.P. and S.S., arXiv:1104.3825 (2011)] is applied to interactions of distinguishable devices. The paper is built around the concept of "doing quantum electrodynamics while thinking classically," which is a generalisation of Sudarshan's renowned optical equivalence theorem [E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)] to the interacting electromagnetic field. This concept allows one to reduce inherently quantum problems to semiclassical considerations.
Using electromagnetic interaction as an example, response transformations [L.P. and S.S., Ann.Phys. 323, 1963, 1989 (2008), 324, 600 (2009)] are applied to the standard perturbative approach of quantum field theory. This approach is rewritten in the form where the place of field propagators is taken by the retarded Green function of the field. Unlike in conventional quantum-field-theoretical techniques, the concept of space-time propagation of quantized field is built into our techniques.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e. using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number $N$ of channels with arbitrary individual capacity i.e. information preservation characteristics in the case of indefinite causal order. We pr…
There have been several experiments which hint at evidence for superluminal transport of electromagnetic energy through a material slab. On the theoretical side, it has appeared evident that acausal signals are indeed possible in quantum electrodynamics. However, it is unlikely that superluminal signals can be understood on the basis of a purely classical electrodynamic signals passing through a material. The classical and quantum theories represent quite different views, and it is the quantum view which may lead to violations of Einstein causality.
Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical spacetime, where the relative order of different nodes is well-defined. In principle, a quantum theory of spacetime could allow the order of the intermediate points between sender and receiver to be in a coherent superposition. Here we experimentally realise a table-top simulation of this exotic possibility on a photonic system, demonstrating high-fidelity t…
We study the information transmission through a quantum channel, defined over a continuous alphabet and losing its energy en route, in presence of correlated noise among different channel uses. We then show that entangled inputs improve the rate of transmission of such a channel.
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 uncover new behaviors of the transmission of information by three quantum channels in superposition of causal orders subject to some level of noise. We find that the transmission can exhibit three different behaviors as the level of noise is varied. This multifold behavior can be explained by the different equivalence classes of quantum switch matrices related to specific combinations of causal orders. We classify these matrices using their characteristic polynomials and matrix invariants, and we calculate analytical expressions for the Holevo information in three representative cases. Our …
Based on the rapid experimental developments of circuit QED, we propose a feasible scheme to simulate a spin-boson model with the superconducting circuits, which can be used to detect quantum Kosterlitz-Thouless (KT) phase transition. We design the spin-boson model by using a superconducting phase qubit coupled with a semi-infinite transmission line, which is regarded as bosonic reservoir with a continuum spectrum. By tuning the bias current or the coupling capacitance, the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit. We also e…
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through an appropriate causal Green's functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls-DeWitt bracket analyzed in the multisymplectic context. Once our star-product is defined we are able to apply the Wigner-Weyl map in order to in…
It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time $t$ gives rise to a distinguished state on the algebra generated by fermionic and bosonic field operators. The proof of positivity of the state is given and representations are constructed.
We show that the non-locality together with the statistical character makes the world statistically separable. The super-luminal signal transmission is impossible. The quantum theory is therefore consistent with the relativity and the causality.
The connection between real-time quantum field theory (RTQFT) [see, e.g., A.\ Kamenev and A.\ Levchenko, Advances in Physics {58} (2009) 197] and phase-space techniques [E.\ Wolf and L.\ Mandel, {\em Optical Coherence and Quantum Optics} (Cambridge, 1995)] is investigated. The Keldysh rotation that forms the basis of RTQFT is shown to be a phase-space mapping of the quantum system based on the symmetric (Weyl) ordering. Following this observation, we define generalised Keldysh rotations based on the class of operator orderings introduced by Cahill and Glauber [Phys.\ Rev.\ {177} (1969) 1882]. …
The Hong-Ou-Mandel effect is generalized to a configuration of n bosons prepared in the n input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.
We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein-Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier's height is enhanced yet remains fin…
The Bohm interpretation of quantum mechanics is applied to a transmission and reflection process in a double potential well. We consider a time dependent periodic wave function and study the particle trajectories. The average time, eventally transmitted particles stay inside the barrier is the average transmission time, which can be defined using the causal interpretation. The question remains whether these transmission times can be experimentally measured.
A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J(ω), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial refle…
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…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements alter the structure of spacetime. Possible experimental tests to verify the suggested spacetime interpretation of quantum entangled states are proposed.
Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels
Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg（卢森堡大学安全、可靠性和信任跨学科中心）；École Nationale Supérieure d’Informatique (ESI)（国立高等信息学院）；Research Institute for Digital Future, Khalifa University of Science and Technology（阿提哈德数字未来研究所）
Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise resilience and data throughput, and lower information loss over different propagation mediums (free space, optical fibre, underwater) as compared to conventional qubits based communication system. However, qudits have been little exploited in literature, owing to their difficulty in transmission and detection. In this paper, for the first time, we develop and f…
We consider a Wheeler delayed-choice experiment based on the Mach-Zehnder Interferometer. Since the development of the causal interpretation of relativistic boson fields there have not been any applications for which the equations of motion for the field have been solved explicitly. Here, we provide perhaps the first application of the causal interpretation of boson fields for which the equations of motion are solved. Specifically, we consider the electromagnetic field. Solving the equations of motion allows us to develop a relativistic causal model of the Wheeler delayed-choice Mach-Zehnder I…
A non-Markovianity measure for quantum channels is introduced based on causality measure - a monotone of causal (temporal) correlations - arising out of the pseudo-density matrix (PDM) formalism which treats quantum correlations in space and time on an equal footing. Using the well known damped Jaynes-Cummings model of a two-level system interacting with a bosonic reservoir at zero temperature as an example, it is shown that breakdown of monotonicity of the causality measure is associated with the revival of temporal (causal) correlations hence with the negativity of the decay rate. Also, a no…
Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource by using an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary measurement over such control state and then we get a perfect teleportation by selecting the optimal measurement on it. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the p…
We show how the entanglement in a wide range of continuous variable non-Gaussian states can be preserved against decoherence for long-range quantum communication through an optical fiber. We apply protection via decoherence-free subspaces and quantum dynamical decoupling to this end. The latter is implemented by inserting phase shifters at regular intervals $Δ$ inside the fiber, where $Δ$ is roughly the ratio of the speed of light in the fiber to the bath high-frequency cutoff. Detailed estimates of relevant parameters are provided using the boson-boson model of system-bath interaction for sil…
Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signalling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be tr…
The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of non-interacting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wavepackets, their time dela…
Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm with polynomial query complexity with respect to the number of systems. We model the causal order with quantum combs, and our algorithms output the order of inputs and outputs that the given process is compatible with. Our algorithm searches for the last input and the last output in the causal order, removes them, and iteratively repeats the above procedure until we get the order of all inputs and outputs. Our method guarantees a polynomial running time for quantum co…
A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the structure of the classical relativity spacetime. A bimetric gravity theory locally has two lightcones, one which describes classical special relativity and a larger lightcone which allows light signals to communicate quantum information between entangled states, after a measurement device detects one of the entangled states. The theory would remove the tension…
We investigate the capacity of bosonic quantum channels for the transmission of quantum information. Achievable rates are determined from measurable moments of the channel by showing that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. Along the way we provide a complete characterization of degradable Gaussian channels and those arising fr…
A theory of quantum state reduction is advanced. It is based on two principles: (1) Gauge decomposition; (2) Maximum entropy. To wit: (1) The reduction decomposition of a state vector is the Schmidt decomposition with respect to the states of a set of (dressed) gauge boson modes; (2) The reduction instant is that of the maximum entropy of a resulting mixed state. The theory determines states undergoing the reduction, its instant, resulting pure states and their probabilities. Applications: (Polarized) photon absorption and transmission, emission, particle detection, reduction of a superpositio…
We study the de Broglie-Bohm interpretation of bosonic relativistic quantum mechanics and argue that the negative densities and superluminal velocities that appear in this interpretation do not lead to inconsistencies. After that, we study particle trajectories in bosonic quantum field theory. A new continuously changing hidden variable - the effectivity of a particle (a number between 0 and 1) - is postulated. This variable leads to a causal description of processes of particle creation and destruction. When the field enters one of nonoverlapping wave-functional packets with a definite number…
The dynamics of relativistic (scalar and vector) bosons through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrodinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff-Snyder-Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.
Gaussian quantum channels have recently attracted a growing interest, since they may lead to a tractable approach to the generally hard problem of evaluating quantum channel capacities. However, the analysis performed so far has always been restricted to memoryless channels. Here, we consider the case of a bosonic Gaussian channel with memory, and show that the classical capacity can be significantly enhanced by employing entangled input symbols instead of product symbols.
