Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.
In a recent comment [arXiv:2112.05658], Grudka and Wójcik object to some of our earlier claims concerning a link between fundamental postulates of quantum theory and special relativity extended to superluminal frames of reference. In this short reply we refute these criticisms.
Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schroedinger equations, e.g. as proposed by Doebner and Goldin, yields a Galilean quantum electrodynamics.
Recently Dragan and Ekert [New. J. Phys 22, 033038, 2020] presented arguments that probabilistic dynamics inherent in the realm of quantum physics is related to the propagation of superluminal particles. Moreover they argue that existence of such particles is a natural consequence of the principle of relativity. We show that the proposed extension of Lorentz transformation can be interpreted in natural way without invoking superluminal phenomena.
Galilean invariant Schrödinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schrödinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.
It is argued that the natural kinematics of the pilot-wave theory is Aristotelian. Despite appearances, Galilean invariance is not a fundamental symmetry of the low-energy theory. Instead, it is a fictitious symmetry that has been artificially imposed. It is concluded that the search for a Lorentz-invariant extension is physically misguided.
Galilean invariance leaves its imprint on the energy spectrum and eigenstates of $N$ quantum particles, bosons or fermions, confined in a bounded domain. It endows the spectrum with a recurrent structure which in capillaries or elongated traps of length $L$ and cross-section area $s_\perp$ leads to spectral gaps $n^2h^2s_\perpρ/(2mL)$ at wavenumbers $2nπs_\perpρ$, where $ρ$ is the number density and $m$ is the particle mass. In zero temperature superfluids, in toroidal geometries, it causes the quantization of the flow velocity with the quantum $h/(mL)$ or that of the circulation along the tor…
This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important parameter to characterize this kind entanglement. ``Beam-like'' entanglement and ``shape-like'' entanglement are contrasted. One example of this kind of entanglement is between between the spin degrees of freedom and the momentum degrees of freedom for a non-relativistic particle. This intraparticle entanglement is Galilean invariant.
We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider U(1) gauge transformations. We find that the hydrodynamic canonical field equations are form-invariant in the case of external gauge functions, but not for nonlinear gauge functionals. Hence, nonlinear gauge potentials are non-trivial potentials which may not be "gauged-away". Notably, for a 1D superfluid, attempting to do so generates the gauge-pressure of th…
We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number n of qubits for large n, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in th…
We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.
We experimentally test invariance properties of the six-photonic-qubits generalization of a singlet state. Our results clearly corroborate with theory. The invariance properties are useful to beat some types of decoherence. We also experimentally detect entanglement in the state using an appropriate witness observable, composed of local observables. Our results clearly indicate that the tested setup, which is very stable, is a good candidate for realization of various multi-party quantum communication protocols. The estimated fidelity of the produced state is very high: it reveals very strong …
Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance -- entanglement assisted invariance. Envariance is a recently discovered symmetry of composite quantum systems, which is at the foundational origin of physics and a quantum phenomenon of pure states. These very easily reproducible and freely accessible experiments on Quantum Experience provide simple tools to study the properties of envariance…
In this work we study the entanglement properties under a Lorentz boost of a pair of spin- 1 massive particles, with spin and momentum as the sole degrees of freedom of the system. Different cases for entanglement between spins and momenta are considered as initial states and it is shown that entanglement between the different degrees of freedom is, in general, not invariant. We analyze the entanglement change in terms of the Wigner rotation induced by the transformation and show that, for the case of spin-1 particles, the relative entanglement change between different states depends strongly …
We analyze multipartite entanglement in systems of spin-1/2 particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which contributes to a physical understanding of entanglement classification. We show that quantum information in a relativistic setting requires the partition of the Hilbert space into particles to be taken seriously. Furthermore, we study exemplary cases and show how the spin and momentum entanglement transforms relativistically in a multipartite setting.
The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that containe…
We study the entanglement dynamics of two qubits, each of which is embedded into its local amplitude-damping reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components, which is much different to the result obtained under the Born-Markovian approximation by C. E. López {\it et al.} [Phys. Rev. Lett. \textbf{101}, 080503 (2008)], and particularly it also satisfies an identity. Our unified treatment includes the previous results as…
Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories, alternative to the current one. This enables one to formulate extrapolations of some important quantum mechanical features via adequate extensions of reciprocal maps relating states of a system with states of its subsystems. These extended maps permit one to generalize i) separability measures to any arbitrary statistical model as well as ii) previous entanglemen…
A striking result from nonrelativistic quantum mechanics is the monogamy of entanglement, which states that a particle can be maximally entangled only with one other party, not with several ones. While there is the exact quantitative relation for three qubits and also several inequalities describing monogamy properties it is not clear to what extent exact monogamy relations are a general feature of quantum mechanics. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. They come about through the curious relation between the nonrelativistic quantum…
Another Bell test "loophole" - imperfect rotational invariance - is explored, and novel realist ideas on parametric down-conversion as used in recent "quantum entanglement" experiments are presented. The usual quantum theory of entangled systems assumes we have rotational invariance (RI), so that coincidence rates depend on the difference only between detector settings, not on the absolute values. Bell tests, as such, do not necessarily require RI, but where it fails the presentation of results in the form of coincidence curves can be grossly misleading. Even if the well-known detection loopho…
We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipar…
We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local operations and classical communication and exemplify the use of the invariance in classifying entangled states. The absolute values of these polynomial invariants are entanglement monotones, thereby allowing entanglement measures to be built. Finally, we discuss the properties of these entanglement measures.
In [M. Walter et al., Science 340, 1205, 7 June (2013)], they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification via polytopes and the eigenvalues of the single-particle states. In this paper, for $4n$ qubits, we show the invariance of algebraic multiplicities (AMs) and geometric multiplicities (GMs) of eigenvalues and the invariance of sizes of Jordan blocks (JBs) of the coefficient matrices under SLOCC. We explore properties of spectra, eigenvectors, generalized eigenvectors, standard Jordan normal forms (SJNFs), and Jordan chains of the coeffi…
The topology of entanglement in multipartite states with translational invariance is discussed in this article. Two global features are foundby which one can distinguish distinct states. These are the cyclic unit and the quantised geometric phase. Furthermore the topology is indicated by the fractional spin. Finally a scheme is presented for preparation of these types of states in spin chain systems, in which the degeneracy of the energy levels characterises the robustness of the states with translational invariance.
We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under adding local ancilla in arbitrary state 3) on mixtures of states possessing local orthogonal flags the function is equal to its average. The result holds for multipartite systems. It is intriguing that the obtained conditions are equalities. The only inequality is hidden in the condition of convexity.
Entanglement is one of the key feature of quantum world and any entanglement measure must satisfy some basic laws. Most important of them is the invariance of entanglement under local unitary operations. We show that this is no longer true with local ${\cal {PT}}$ symmetric unitary operations. If two parties share a maximally entangled state, then under local ${\cal {PT}}$ symmetric unitary evolution the entropy of entanglement for pure bipartite states does not remain invariant. Furthermore, we show that if one of the party has access to ${\cal {PT}}$-symmetric quantum world, then a maximally…
Space-time wave packets are propagation-invariant pulsed beams that travel in free space without diffraction or dispersion by virtue of tight correlations introduced into their spatio-temporal spectrum. Such correlations constitute an embodiment of classical entanglement between continuous degrees of freedom. Using a measure of classical entanglement based on the Schmidt number of the field, we demonstrate theoretically and experimentally that the degree of classical entanglement determines the diffraction-free propagation distance of ST wave packets. Reduction in the degree of classical entan…
We study the mechanism by which the particle-antiparticle entangled state collapses instantaneously at a distance. By making two key assumptions, we are able to show not only that instantaneous collapse of a wave function at a distance is possible but also that it is an invariant quantity under Lorentz transformation and compatible with relativity. In addition, we will be able to detect in which situation a many-body entangled system exhibits the maximum collapse speed among its entangled particles. Finally we suggest that every force in nature acts via entanglement.
Quantum Work Statistics from Entanglement-Assisted Invariance
University of Massachusetts, Boston（马萨诸塞大学波士顿分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩分校量子科学研究所）
This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an S-matrix that respects certain symmetries and the entanglement of the pure out-state is measured. The analysis is phrased in terms of unitary, irreducible representations (UIRs) of the symmetry group in question, either the rotation group for the spin degrees of freedom or the Galilean group for non-relativistic particles. Entanglement may occurs when multip…
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space-time when $Σ$ is sphere $S_2$ and when $Σ$ is two-dimensional cylinder. The contribution of the type A conformal anomaly to ent…
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and their behaviour under the Lorentz group are analysed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transfo…
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under the Galilean group, the invariance is usually not discussed in the case of the interpretation of the theory. This situation is particularly pressing for realist positions, which want to know how reality would be if quantum mechanics were true. From a realist perspective, it seems reasonable to require that an interpretation of quantum mechanics, to be admissib…
