For a generic interferometer, the conditional probability density distribution, p(φ|m), for the phase φ given measurement outcome m, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as ∆φ ∼ 1/ √ N (the standard limit), or ∆φ ∼ 1/N (the Heisenberg limit). We propose an alternative measure of phase sensitivity-the fidelity of an interferometer-defined as the Shannon mutual information between the phase shift φ and the measurement outcomes m. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled N00N state input leads to a lower fidelity than a Fock state input, for the same photon number. Introduction.Phase sensitivity of interferometers has been a topic of research for many years because of interest in the fundamental limitations of measurement [1, 2], gravitational-wave detection [3], and optical [4,5], atom [6], and Bose-Einstein condensate(BEC)-based gyroscopes [7,8,9]. Recently, applications to sensors are being explored [10,11].The phase sensitivity of interferometers is believed to be limited by quantum fluctuations [12], and the phase sensitivity of various interferometers has been explored for different types of input states, such as squeezed states [12,13], and number states [14,15,16,17,18,19,20,21,22]. In all the above cases, the phase sensitivity ∆φ has been discussed in terms of two limits, known as the standard limit, ∆φ SL = 1/ √ N , and the Heisenberg limit[23], ∆φ HL = 1/N , where N is the number of particles that enter the interferometer during each measurement cycle. These arguments are based on results of standard estimation theory [24] which connects an ensemble of measurement outcomes, m i , i = 1, 2, · · · , M , with corresponding phases, φ i , through a theoretical relation m = m(φ). An example of the theoretical relation associated with some quantum observable is m(φ) = φ| m|φ , where the state is parameterized by a single parameter φ. Standard estimation theory predicts that the standard deviation, ∆φ, of the probability distribution for the phase φ, is related to the standard deviation in the measurements, ∆m, by [24]

A communication protocol is introduced that allows the receiver of a message to place an a posteriori bound on the amount of information that an eavesdropper could have obtained during transmission of that message. This quantum cryptographic protocol is distinct from quantum key distribution. The quantum states and measurements required by this protocol are simple enough that it can be implemented using existing technology.A major concern when transmitting a secret message over a public communication channel is that an eavesdropper might intercept the message and learn its meaning. This is combatted by encrypting the message so that an eavesdropper cannot decipher the meaning of the intercepted message. [1,2] In its most secure form, this relies upon the communicating parties sharing a single-use private key which is as long as the message.[1] Recently, great strides have been made at generating and distributing private keys using quantum mechanical systems sent through insecure channels.[3] Such quantum key generation (QKD) protocols have the distinct feature that an eavesdropper leaves evidence of her activity. However, due to their design, these QKD protocols do not convey messages.In this Letter we introduce a quantum seal protocol, which is a method for two parties to communicate a message, not simply to generate a random key. [4,5] Its utility comes from the fact that it allows the receiver to place an a posteriori bound on the amount of information an eavesdropper could have obtained over the course of the transmission. Each time a message is sent, there is a straightforward way in which an eavesdropper can attempt to intercept the message. Yet if this occurs, the receiver will be given an unambiguous indication that there was a disturbance in the system and an eavesdropper may have been tapping into the communication channel. If there is no eavesdropper and the quantum channel is relatively noise-free, then the receiver will have confidence that no other parties have read the message.This protocol can be used to seal up and communicate an encrypted message, thereby providing an extra layer of assurance while sending sensitive material, on top of any sophisticated encryption technique that may currently be used.The protocol involves a message sender, named Alice, trying to get a message bit b (whose values can be zero or one) to a receiver, called Bob. The entire process is initiated by Alice announcing that she has a message she wants to communicate to Bob. Then a routine is repeated many times. Each repetition is referred to as a single "shot", and proceeds as follows.Bob starts the routine by preparing some physical sys- Bit-Announcements Result-Announcementstem (which we refer to as a particle) in one of four quantum states, represented by density matrices(Here we have used the standard notation for a qubit Hilbert space that is spanned by basis vectors |0 and |1 and |± ≡ 2Bob employs a randomized method of preparation so that he is equally likely to prepare the particle in any of these four states. B...

No abstract

Abstract. A quantum protocol is described which enables a user to send sealed messages and that allows for the detection of active eavesdroppers. We examine a class of eavesdropping strategies, those that make use of quantum operations, and we determine the information gain versus disturbance caused by these strategies. We demonstrate this tradeoff with an example and we compare this protocol to quantum key distribution, quantum direct communication, and quantum seal protocols.