We perform a mathematical analysis of the classical computational complexity of two genuine quantum-mechanical problems, which are inspired in the calculation of the expected magnetizations and the entanglement between subsystems for a quantum spin system. These problems, which we respectively call SES and SESSP, are specified in terms of pure slightly-entangled quantum states of n qubits, and rigorous mathematical proofs that they belong to the NP-Complete complexity class are presented. Both SES and SESSP are, therefore, computationally equivalent to the relevant 3-SAT problem, for which an efficient algorithm is yet to be discovered.
The possibility of generating a multi-hops network between different entangled nodes (qubits) via spin Dipolar interaction is examined. The negativity, tangle and the non-local coherent advantage are used as quantifiers of the generated quantum correlations. The phenomena of the sudden death/birth is displayed for the entangled two nodes, while the sudden changes phenomena (increasing/ decreasing) is depicted for all entangled three nodes. The amount of correlations between the different nodes depend on the initial network settings, where the largest amount is predicted if the network is initi…
We review some semantical aspects of probability bounds from Boole's "conditions on possible experience" violated by quantum mechanics. We also speculate about emerging space-time categories as an epiphenomenon of quantization and the resulting breakdown of relativity theory by non-unitary and non-linear processes.
Some forms of classical simulations of quantum type probabilities and correlations are capable of violating Boole's conditions of possible experience, such as the Clauser-Horne-Shimony-Holt inequality, even beyond the Tsirelson bound. This can be achieved by communicating a single bit encoding the measurement context.
We investigate the phase enhancement of quantum states subject to non-linear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states and of odd ECS states with the same average particle number <n> and non-linearity exponent k. We investigate the creation of approximate ECSs (AECSs) from a squeezed vacuum with current optical technology methods and find that a pure AECS is even slightly better than an even ECS for large <n>. We also examine simple but physically relevant cases of loss in the non-linear interferometer arm…
In their 2002 article, Ghirardi, Marinatto and Weber have proposed a formal analysis of the entanglement properties for a system consisting of N distinguishable particles. Their analysis leads to the differentiation of three possible situations that can arise in such systems: complete entanglement, complete non-entanglement, and the remaining cases. I argue that this categorization leaves out one important possibility in which a system is completely entangled, and yet some of its subsystems are mutually non-entangled. As an example I present and discuss a state of a three-particle system which…
We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum eraser (QE) utilizing a Mach-Zehnder interferometer with a variable partially-polarizing beam splitter (VPPBS) at the input. The use of the VPPBS motivates us to introduce the entangled quantum eraser, for which the path information is erased using a Bell-basis measurement. We also investigate the behavior of the wave aspect, i.e., the quantum coherence, as well as the particle character, represented by the predictability and entanglement, as delineated in complete complementarity relations (CCRs). A…
With a probability of success of $95 \%$ we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally lacks an efficient solution due to the existence of bound entangled states. In contrast to free entangled states that can be used for entanglement distillation via local operations and classical communication, these states cannot be detected by the Peres-Horodecki criterion or PPT criterion. We analyze a large family of bipartite qutrit states that can be sepa…
Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two s…
A new kind of tripartite non-symmetric coordinate coherent-entangled state (TNCCES) $ | β,γ,x >$ is proposed which exhibits the properties of both coherence and entanglement and makes up a new quantum mechanical representation.We investigate some properties of TNCCES such as completeness and orthogonality which prove it is just a tripartite complete continuous coordinate base. A protocol for generating TNCCES is proposed using asymmetric beam splitter. And in application of TNCCES, we find its corresponding Wigner operator and carry out its marginal distribution form; further a new tripartite …
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in the sense that every entangled subspace is shown to be so at some finite level of the hierarchy. It generalizes straightforwardly to the case of higher Schmidt rank, as well as the multipartite cases of completely and genuinely entangled subspaces. These hierarchies work extremely well in practice even in very large quantum systems, as they can be implemente…
In this work, we study the quantum Fisher information (QFI) per particle of an open (particles can enter and leave the system) and dissipative (far from thermodynamical equilibrium) steady state system of two qubits in noisy channels. We concentrate on two noisy channels these are dephasing and non-dephasing channels. We will show that under certain conditions QFI per particle is slightly greater than 1 for both systems. This means that both systems can be slightly entangled.
We show that a physical property can be entirely separated from the object it belongs to, hence realizing a complete quantum Cheshire cat. Our setup makes use of a type of quantum state of particular interest, namely an entangled pre- and post-selected state, in which the pre- and post-selections are entangled with each other. Finally we propose a scheme for the experimental implementation of these ideas.
Integrated optics allow the generation and control of increasingly complex photonic states on chip based architectures. Here, we implement two entangled qutrits - a 9-dimensional quantum system - and demonstrate an exceptionally high degree of experimental control. The approach which is conceptually different to common bulk optical implementations is heavily based on methods of integrated in-fiber and on-chip technologies and further motivated by methods commonly used in today's telecommunication industry. The system is composed of an in-fiber source creating entangled qutrit states of any amp…
Telecloning and its reverse process, referred to as remote information concentration(RIC), have attracted considerable interest because of their potential applications in quantum-information processing. We here present a general scheme for RIC in d-level systems (qudits), in which the quantum information initially distributed in many spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. We show that the entangled channel of RIC can be different types of entangled states, including mixed…
Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocl, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve …
Recently demonstrated ghost interference using correlated photons of different frequencies, has been theoretically analyzed. The calculation predicts an interesting nonlocal effect: the fringe width of the ghost interference depends not only on the wave-length of the photon involved, but also on the wavelength of the other photon with which it is entangled. This feature, arising because of different frequencies of the entangled photons, was hidden in the original ghost interference experiment. This prediction can be experimentally tested in a slightly modified version of the experiment.
The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the app…
The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arbitrary joint unitary on the system and environment; the other concerned with specific initial states that may be highly entangled. Here we study the latter problem, and highlight the interplay between the initial correlations and the unitary applied.…
We prove that as conjectured by Ac\'ın et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.
We study broadband polarization entangled states generated within the line width of type-II Spontaneous Parametric Down Conversion (SPDC). Applying a complete quantum polarization tomography protocol at arbitrary combination of frequency and angular sideband modes we reveal a complex structure of non-degenerate non-collinear polarization entangled states generated within the SPDC line width. It is demonstrated that simultaneous compensation of longitudinal and transverse walk off leads to homogenizing the structure of polarization entanglement.
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testin…
A new kind of tripartite coherent-entangled state (CES) $\ket{β,γ, x}_{μντ}$ is proposed, which exhibits the properties of both coherence and entanglement. We investigate its completeness and orthogonality, and find it can make up a representation of tripartite CES. A protocol for generating the tripartite CES is proposed using asymmetric beam splitter. Applications of the tripartite CES in quantum optics are also presented.
We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical communication. The corresponding minimal quantum coherence is the entanglement of formation. Connections to the relative entropy of entanglement and quantum coherence, and generalizations to the multiparty case are also considered.
We investigate performances of pure continuous variable states in discriminating thermal and identity channels by comparing their M-copy error probability bounds. This offers us a simplified mathematical analysis for quantum target detection with slightly modified features: the object -- if it is present -- perfectly reflects the signal beam irradiating it, while thermal noise photons are returned to the receiver in its absence. This model facilitates us to obtain analytic results on error-probability bounds i.e., the quantum Chernoff bound and the lower bound constructed from the Bhattacharya…
We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat mirrors. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transitions rates from the entangled states to the collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between th…
We show that using a slightly modified XX model for a spin-1/2 chain, one can transmit almost perfectly a maximally entangled two-qubit state from one end of the chain to the other one. This is accomplished without external fields or modulation of the coupling constants among the qubits. We also show that this strategy works for any size of the chain and is relatively robust to imperfections in the coupling constants among the qubits belonging to the chain. Actually, under certain scenarios of small disorder, we obtain better results than those predicted by the optimal ordered and noiseless ca…
Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure state. Among CESs one finds a class of subspaces in which all vectors are not only entangled, but are genuinely entangled. Here we explore the connection between UPBs…
For carrying out many quantum information protocols entanglement must be established in advance between two distant parties. Practically, inevitable interaction of entangled subsystems with their environments during distribution and storage will result in degradation of entanglement. Here we investigate the decoherence of two-qubit entangled states in the local amplitude noise. We show that there exists a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction, and quan…
Complete Existence Classification of Seven-Partite Absolutely Maximally Entangled States
School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机学院）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息与计算倡议）
By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.
Maximally entangled states play a central role in quantum information processing. Despite much progress throughout the years, robust protocols for manipulations of such states in many-level systems are still scarce. Here we present a control scheme that allow efficient manipulation of complete population transfer between two maximally entangled states. Exploiting the self-duality of $\mathrm{SU}\left(2\right)$, we present in this work a family of ${\mathrm{2}}^{\mathrm{2}N}$-level systems with couplings related to Pythagorean triples that make a complete population transfer from one state to a…
In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror mo…
The Minimal Dimension of Entangled-Noise Advantage
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院，先进微结构协同创新中心）
We study the locally unextendible non-maximally entangled basis (LUNMEB) in $H^{d}\bigotimes H^{d}$. We point out that there exists an error in the proof of the main result of LUNMEB [Quant. Inf. Comput. 12, 0271(2012)], which claims that there are at most $d$ orthogonal vectors in a LUNMEB, constructed from a given non-maximally entangled state. We show that both the proof and the main result are not correct in general. We present a counter example for $d=4$, in which five orthogonal vectors from a specific non-maximally entangled state are constructed. Besides, we completely solve the proble…
