We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error.
We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.
We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglement, and involves only single copy measurements.
We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigati…
Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 an…
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing the entanglement witnesses based on second moments, and use them in a semidefinite program providing the optimal entanglement test for given random measurements. We test the method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices.
We develop a theory to teleport an unknown quantum state using entanglement between two distant parties. Our theory takes into account experimental limitations due to contribution of multi-photon pair production of parametric down conversion source, inefficiency and dark counts of detectors and channel losses. We use a linear optics setup for quantum teleportation of an unknown quantum state by performing Bell state measurement by the sender. Our theory successfully provides a model for experimentalists to optimize the fidelity by adjusting the experimental parameters. We apply our model to a …
One of the essential building blocks of classical computer programs is the "if" clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the…
Like entanglement, quantum discord quantifies the quantum correlations. Unlike entanglement, whose detection is extremely difficult, the quantum discord of an arbitrary bipartite state allows itself to be detected perfectly by a single observable, the quantum discord witness. In particular, we report a single observable whose expectation value provides a necessary and sufficient condition for the vanishing quantum discord of an arbitrary bipartite unknown state with four copies. A quantum circuit is designed to measure the quantum discord witness by using only local qubit-measurements.
The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this paper we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not o…
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a "collective" impossibility on multiple quantum states while most other "no-go" theorems concern with only one single state each time, i.e., it is an impossibility on a non-local quantum operation. This novel impossibility may provide a new insight into the nature of quantum mechanics and it i…
We present setups for the practical realization of adding control to unknown subroutines, supplementing the existing quantum optical scheme for black-box control with a counterpart for the quantum control of the ordering of sequences of operations. We also provide schemes to realize either task using trapped ions. These practical circumventions of recent no-go theorems are based on existing technologies. We argue that the possibility to add control to unknown operations in practice is a common feature of many physical systems. Based on the proposed implementations we discuss the apparent contr…
A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalizati…
Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by any observables directly. In this paper, we train neural networks to quantify unknown entanglement, where the input features of neural networks are the outcome statistics data produced by locally measuring target quantum states, and the training labels are well-chosen quantities. For bipartite quantum states, this quantity is coherent information, which is a…
We propose and develop theory of quantum teleportation of unknown qubit based on interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components of the hybrid, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary modes
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be already characterized. We break this loop by designing an operational framework able to optimally characterize any given unknown quantum channel in a device-independent fashion, namely, by only looking at its input-output statistics, under the sole assumption that quantum theory is valid. We provide explicit solutions, in closed form, for practically relevant cas…
Simultaneous Detection of High-Dimensional Entanglement for Two Unknown Quantum States
School of Mathematics, South China University of Technology（华南理工大学数学学院）；College of Information Science and Technology, Jinan University（暨南大学信息科学技术学院）；School of Mathematics, Guangdong University of Education（广东第二师范学院数学学院）；School of Science, Jimei University（集美大学理学院）；School of Physics and Optoelectronics Engineering, Anhui University（安徽大学物理与光电工程学院）；School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University（上海交通大学数学科学学院教育部重点实验室）；Shanghai Seres Information Technology Co., Ltd（上海赛力斯信息技术有限公司）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学深圳量子科学与工程研究院）；School of Computer Science and Technology, Dongguan University of Technology（东莞理工学院计算机科学与技术学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）；Max-Planck-Institute for Mathematics in the Sciences（德国马普科学数学研究所）；Naturwissenschaftlich-Technische Fakultät, Universität Siegen（锡根大学自然科学技术学院）
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for nonzero quantum discord in $2\times N$ systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same easy manner as that of the entanglement witness, moreover a quant…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the use of random local measurements, from which entanglement witnesses are then constructed via semidefinite programming methods. We propose a scheme of successively increasing the number of measurements until the presence of entanglement can be unambiguously concluded, and investigate its performance in various examples.
In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence of closed time like curves, one can indeed create superposition of unknown quantum states and evade the no-go result.
The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work we systematically study the problem of creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, we provide an explicit probabilistic protocol generating a superposition of two unknown …
In this paper, we consider the problem of open-loop control of a qubit that is coupled to an unknown fully quantum non-Markovian noise (either bosonic or fermionic). A graybox model that is empirically obtained from measurement data is employed to approximately represent the unknown quantum noise. The estimated model is then used to calculate the open-loop control pulses under constraints on the pulse amplitude and timing. For the control pulse optimization, we explore the use of gradient descent and genetic optimization methods. We consider the effect of finite sampling on estimating expectat…
