No Arabic abstract
We study sequential state discrimination measurements performed on the same qubit by subsequent observers. Specifically, we focus on the case when the observers perform a kind of a minimum-error type state discriminating measurement where the goal of the observers is to maximize their joint probability of successfully guessing the state that the qubit was initially prepared in. We call this the joint best guess strategy. In this scheme, Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, and so on to altogether N consecutive receivers who all perform measurements on it. The goal for all observers is to determine which state Alice sent. In the joint best guess strategy, every time a system is received the observer is required to make a guess, aided by the measurement, about its state. The price to pay for this requirement is that errors must be permitted, the guess can be correct or in error. There is a nonzero probability for all the receivers to successfully identify the initially prepared state, and we maximize this joint probability of success. This work is a step toward developing a theory of nondestructive sequential quantum measurements and could be useful in multiparty quantum communication schemes based on communicating with single qubits, particularly in schemes employing continuous variable states. It also represents a case where subsequent observers can probabilistically and optimally get around both the collapse postulate and the no-broadcasting theorem.
There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations that support the recent Conjecture in [S. Cheng {it et al.}, arXiv:2102.11574], that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot. We also answer a question raised in [P. J. Brown and R. Colbeck, Phys. Rev. Lett. textbf{125}, 090401 (2020)], by showing that the conditions given therein for the recycling of one qubit by an arbitrarily large number of observers are sufficient but not necessary. Finally, we find that it is possible to share Bell nonlocality between multiple pairs of independent observers on both sides, if sufficiently many pairs of qubits are shared. Our results are based on a formalism that is applicable to more general problems in recycling entanglement, and hence is expected to aid progress in this field.
Non-local Advantage of Quantum Coherence(NAQC) or steerability of local quantum coherence is a strong non-local resource based on coherence complementarity relations. In this work, we provide an upper bound on the number of observers who can independently steer the coherence of the observer in the other wing in a scenario where half of an entangled pair of spin-$frac{1}{2}$ particles is shared between a single observer (Bob) in one wing and several observers (Alices) on the other, who can act sequentially and independently of each other. We consider one-parameter dichotomic POVMs for the Alices and mutually unbiased basis in which Bob measures coherence in case of the maximally entangled bipartite qubit state. We show that not more than two Alices can exhibit NAQC when $l_1$-norm of coherence measure is probed, whereas for two other measures of coherence, only one Alice can reveal NAQC within the same framework.
We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding one-sided monogamy relations that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum reversibilities of qubit measurements. We also show if the assumptions are relaxed to allow sufficiently biased measurement selections, then there is a narrow range of measurement strengths that allows two-sided recycling for two observers on each side, and propose an experimental test. Our methods may be readily applied to other types of quantum correlations, such as steering and entanglement, and hence to general information protocols involving sequential measurements.
We investigate the trade-off between information gain and disturbance for a class of weak von Neumann measurements on spin-$frac{1}{2}$ particles, and derive the unusual measurement pointer state that saturates this trade-off. We then consider the fundamental question of sharing the non-locality of a single particle of an entangled pair among multiple observers, and demonstrate that by exploiting the information gain disturbance trade-off, one can obtain an arbitrarily long sequence of consecutive and independent violations of the CHSH-Bell inequality.
A quantum battery is a work reservoir that stores energy in quantum degrees of freedom. When immersed in an environment an open quantum battery needs to be stabilized against free energy leakage into the environment. For this purpose we here propose a simple protocol that relies on projective measurement and obeys a second-law like inequality for the battery entropy production rate.