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55-513: QSS may refer to: Quantum Secret Sharing , a quantum cryptographic scheme for secure communication Queensway Secondary School , a co-educational government secondary school in Queenstown, Singapore QSS, the station code for Qila Sattar Shah railway station , Sheikhupura District, Pakistan Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

110-609: A rectangle . Later, they came to mean a right triangle . In the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle. In mathematics , orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms . Two elements u and v of a vector space with bilinear form B {\displaystyle B} are orthogonal when B ( u , v ) = 0 {\displaystyle B(\mathbf {u} ,\mathbf {v} )=0} . Depending on

165-601: A "pseudo-GHZ state" where the difference from a true GHZ state is that the three photons do not exist simultaneously. Nonetheless, the triple "coincidences" can be described by exactly the same probability function as for the true GHZ state, implying that QSS will work just the same for this 2-particle source. By setting the phases α , β , {\displaystyle \alpha ,\beta ,} and γ {\displaystyle \gamma } to either 0 or π 2 {\displaystyle {\frac {\pi }{2}}} in much

220-472: A , g , and n ) versions of 802.11 Wi-Fi ; WiMAX ; ITU-T G.hn , DVB-T , the terrestrial digital TV broadcast system used in most of the world outside North America; and DMT (Discrete Multi Tone), the standard form of ADSL . In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that crosstalk between the subchannels is eliminated and intercarrier guard bands are not required. This greatly simplifies

275-403: A basis to measure in, and half of the time she will choose the wrong basis. When she chooses the correct basis, she will get the correct measurement result with certainty and can recreate the state she measured and send it off to Bob without her presence being detected. However, when she chooses the wrong basis, she will end up sending one of the two states from the incorrect basis. Bob will measure

330-546: A cryptographic key that only they know. The simple case described above can be extended similarly to that done in CSS by Shamir and Blakley via a thresholding scheme. In the (( k , n )) threshold scheme (double parentheses denoting a quantum scheme), Alice splits her secret key (quantum state) into n shares such that any k≤n shares are required to extract the full information but k-1 or less shares cannot extract any information about Alice's key. The number of users needed to extract

385-596: A joint key for communicating securely. Consider the following for a clear example of how this will work. Let us define the x and y eigenstates in the following, standard way: The GHZ state can then be rewritten as where (a, b, c) denote the particles for (Alice, Bob, Charlie) and Alice's and Bob's states have been written in the X-basis. Using this form, it is evident that their exists a correlation between Alice's and Bob's measurements and Charlie's single-particle state: if Alice and Bob have correlated results then Charlie has

440-513: A participant's interferometer, this notation describes the arbitrary path taken for any combination of two participants. Notice that | S ⟩ A , | L ⟩ j {\displaystyle |\mathrm {S} \rangle _{A},|\mathrm {L} \rangle _{j}} and | L ⟩ A , | S ⟩ j {\displaystyle |\mathrm {L} \rangle _{A},|\mathrm {S} \rangle _{j}} where j

495-457: A sender who wishes to share a secret with a number of receiver parties in such a way that the secret is fully revealed only if a large enough portion of the receivers work together. However, if not enough receivers work together to reveal the secret, the secret remains completely unknown. The classical scheme was independently proposed by Adi Shamir and George Blakley in 1979. In 1998, Mark Hillery, Vladimír Bužek, and André Berthiaume extended

550-414: A simple ((2,3)) threshold scheme, and more complicated schemes can be imagined by increasing the number of shares Alice splits her original state into: Consider Alice beginning with the single qutrit state and then mapping it to three qutrits and sharing one qutrit with each of the 3 receivers. It is evident that a single share does not give any information about Alice's original state, since each share

605-487: A time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis of simultaneous events, also determined by the rapidity. The theory features relativity of simultaneity . In quantum mechanics , a sufficient (but not necessary) condition that two eigenstates of a Hermitian operator , ψ m {\displaystyle \psi _{m}} and ψ n {\displaystyle \psi _{n}} , are orthogonal

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660-448: Is time-division multiple access (TDMA), where the orthogonal basis functions are nonoverlapping rectangular pulses ("time slots"). Another scheme is orthogonal frequency-division multiplexing (OFDM), which refers to the use, by a single transmitter, of a set of frequency multiplexed signals with the exact minimum frequency spacing needed to make them orthogonal so that they do not interfere with each other. Well known examples include (

715-464: Is a strategy allowing the deprotection of functional groups independently of each other. In supramolecular chemistry the notion of orthogonality refers to the possibility of two or more supramolecular, often non-covalent , interactions being compatible; reversibly forming without interference from the other. In analytical chemistry , analyses are "orthogonal" if they make a measurement or identification in completely different ways, thus increasing

770-459: Is acting as a malicious user by trying to obtain the secret without the other participants being aware. Analyzing the possibilities, one learns that choosing the proper order in which Bob and Charlie release their measurement bases and results when testing for eavesdropping can promise the detection of any cheating that may be occurring. The proper order turns out to be: This ordering prevents receiver 2 from knowing which basis to share for tricking

825-417: Is called an orthogonal map. In philosophy , two topics, authors, or pieces of writing are said to be "orthogonal" to each other when they do not substantively cover what could be considered potentially overlapping or competing claims. Thus, texts in philosophy can either support and complement one another, they can offer competing explanations or systems, or they can be orthogonal to each other in cases where

880-415: Is clear from the table summarizing these correlations that by knowing the measurement bases of Alice and Bob, Charlie can use his own measurement result to deduce whether Alice and Bob had the same or opposite results. Note however that to make this deduction, Charlie must choose the correct measurement basis for measuring his own particle. Since he chooses between two noncommuting bases at random, only half of

935-416: Is easier to verify designs that neither cause side effects nor depend on them. An instruction set is said to be orthogonal if it lacks redundancy (i.e., there is only a single instruction that can be used to accomplish a given task) and is designed such that instructions can use any register in any addressing mode . This terminology results from considering an instruction as a vector whose components are

990-612: Is either 'B' or 'C' are indistinguishable processes as the time difference between the two processes are exactly the same. The same is true for | S ⟩ B , | S ⟩ C {\displaystyle |\mathrm {S} \rangle _{B},|\mathrm {S} \rangle _{C}} and | L ⟩ B , | L ⟩ C . {\displaystyle |\mathrm {L} \rangle _{B},|\mathrm {L} \rangle _{C}.} Describing these indistinguishable processes mathematically, which can be thought of as

1045-413: Is in the maximally mixed state. However, two shares could be used to reconstruct Alice's original state. Assume the first two shares are given. Add the first share to the second (modulo three) and then add the new value of the second share to the first. The resulting state is where the first qutrit is exactly Alice's original state. Via this method, the sender's original state can be reconstructed at one of

1100-554: Is perpendicular to line B"), orthogonal is commonly used without to (e.g., "orthogonal lines A and B"). Orthogonality is also used with various meanings that are often weakly related or not related at all with the mathematical meanings. The word comes from the Ancient Greek ὀρθός ( orthós ), meaning "upright", and γωνία ( gōnía ), meaning "angle". The Ancient Greek ὀρθογώνιον ( orthogṓnion ) and Classical Latin orthogonium originally denoted

1155-403: Is receiver 1 or receiver 2. Thus, the ordering of releasing the data must be carefully chosen so as to prevent any dishonest user from acquiring the secret without being noticed by the other participants. This section follows from the first experimental demonstration of QSS in 2001 which was made possible via advances in techniques of quantum optics . The original idea for QSS using GHZ states

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1210-520: Is that they correspond to different eigenvalues. This means, in Dirac notation , that ⟨ ψ m | ψ n ⟩ = 0 {\displaystyle \langle \psi _{m}|\psi _{n}\rangle =0} if ψ m {\displaystyle \psi _{m}} and ψ n {\displaystyle \psi _{n}} correspond to different eigenvalues. This follows from

1265-568: The web site of the Thyssen-Bornemisza Museum states that "Mondrian ... dedicated his entire oeuvre to the investigation of the balance between orthogonal lines and primary colours." Archived 2009-01-31 at the Wayback Machine Orthogonality in programming language design is the ability to use various language features in arbitrary combinations with consistent results. This usage was introduced by Van Wijngaarden in

1320-497: The Bell-type inequality was violated, with S e x p = 3.69 {\displaystyle S_{\rm {exp}}=3.69} , suggesting that this setup exhibits quantum nonlocality . This seminal experiment showed that the quantum correlations from this setup are indeed described by the probability function P i , j , k . {\displaystyle P_{i,j,k}.} The simplicity of

1375-501: The SPDC source allowed for coincidences at much higher rates than traditional three-photon entanglement sources, making QSS more practical. This was the first experiment to prove the feasibility of a QSS protocol. Orthogonality In mathematics , orthogonality is the generalization of the geometric notion of perpendicularity . Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A

1430-455: The X- or Y-basis (chosen at random), they share (via a classical, public channel ) which basis they used to make the measurement, but not the result itself. Upon combining their measurement results, Bob and Charlie can deduce what Alice measured 50% of the time. Repeating this process many times, and using a small fraction to verify that no malicious actors are present, the three participants can establish

1485-612: The bilinear form, the vector space may contain null vectors , non-zero self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality . In the case of function spaces , families of functions are used to form an orthogonal basis , such as in the contexts of orthogonal polynomials , orthogonal functions , and combinatorics . In optics , polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization . In special relativity ,

1540-418: The design of Algol 68 : The number of independent primitive concepts has been minimized in order that the language be easy to describe, to learn, and to implement. On the other hand, these concepts have been applied “orthogonally” in order to maximize the expressive power of the language while trying to avoid deleterious superfluities. Orthogonality is a system design property which guarantees that modifying

1595-400: The design of both the transmitter and the receiver. In conventional FDM, a separate filter for each subchannel is required. When performing statistical analysis, independent variables that affect a particular dependent variable are said to be orthogonal if they are uncorrelated, since the covariance forms an inner product. In this case the same results are obtained for the effect of any of

1650-478: The exact same way as quantum key distribution. Consider an eavesdropper, Eve, who is assumed to be capable of perfectly discriminating and creating the quantum states used in the QSS protocol. Eve's objective is to intercept one of the receivers' (say Bob's) shares, measure it, then recreate the state and send it on to whomever the share was initially intended for. The issue with this method is that Eve needs to randomly choose

1705-420: The explanatory variables and model residuals. In taxonomy , an orthogonal classification is one in which no item is a member of more than one group, that is, the classifications are mutually exclusive. In chemistry and biochemistry, an orthogonal interaction occurs when there are two pairs of substances and each substance can interact with their respective partner, but does not interact with either substance of

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1760-846: The fact that Schrödinger's equation is a Sturm–Liouville equation (in Schrödinger's formulation) or that observables are given by Hermitian operators (in Heisenberg's formulation). In art, the perspective (imaginary) lines pointing to the vanishing point are referred to as "orthogonal lines". The term "orthogonal line" often has a quite different meaning in the literature of modern art criticism. Many works by painters such as Piet Mondrian and Burgoyne Diller are noted for their exclusive use of "orthogonal lines" — not, however, with reference to perspective, but rather referring to lines that are straight and exclusively horizontal or vertical, forming right angles where they intersect. For example, an essay at

1815-525: The geometric sense discussed above, both as observed data (i.e., vectors) and as random variables (i.e., density functions). One econometric formalism that is alternative to the maximum likelihood framework, the Generalized Method of Moments , relies on orthogonality conditions. In particular, the Ordinary Least Squares estimator may be easily derived from an orthogonality condition between

1870-454: The independent variables upon the dependent variable, regardless of whether one models the effects of the variables individually with simple regression or simultaneously with multiple regression . If correlation is present, the factors are not orthogonal and different results are obtained by the two methods. This usage arises from the fact that if centered by subtracting the expected value (the mean), uncorrelated variables are orthogonal in

1925-448: The instruction fields. One field identifies the registers to be operated upon and another specifies the addressing mode. An orthogonal instruction set uniquely encodes all combinations of registers and addressing modes. In telecommunications , multiple access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions . One such scheme

1980-428: The left and right stereo channels in a single groove. The V-shaped groove in the vinyl has walls that are 90 degrees to each other, with variations in each wall separately encoding one of the two analogue channels that make up the stereo signal. The cartridge senses the motion of the stylus following the groove in two orthogonal directions: 45 degrees from vertical to either side. A pure horizontal motion corresponds to

2035-403: The original scheme laid out by Hillery et al. in 1998 which makes use of Greenberger–Horne–Zeilinger (GHZ) states . A similar scheme was developed shortly thereafter which used two-particle entangled states instead of three-particle states. In both cases, the protocol is essentially an extension of quantum key distribution to two receivers instead of just one. Following the typical language, let

2090-481: The other pair. For example, DNA has two orthogonal pairs: cytosine and guanine form a base-pair, and adenine and thymine form another base-pair, but other base-pair combinations are strongly disfavored. As a chemical example, tetrazine reacts with transcyclooctene and azide reacts with cyclooctyne without any cross-reaction, so these are mutually orthogonal reactions, and so, can be performed simultaneously and selectively. In organic synthesis , orthogonal protection

2145-416: The other participants because receiver 2 does not yet know what basis receiver 1 is going to announce was used. Similarly, since receiver 1 must release their results first, they cannot control if the measurements should be correlated or anticorrelated for the valid combination of bases used. In this way, acting dishonestly will introduce errors in the eavesdropper testing phase whether the dishonest participant

2200-401: The prone to error device or method. The failure mode of an orthogonally redundant back-up device or method does not intersect with and is completely different from the failure mode of the device or method in need of redundancy to safeguard the total system against catastrophic failure. In neuroscience , a sensory map in the brain which has overlapping stimulus coding (e.g. location and quality)

2255-414: The protocol errors occurring with a 75% probability instead of the 50% probability predicted by the theory, thus signaling that there is an eavesdropper within the communication channel. More complex eavesdropping strategies can be performed using ancilla states, but the eavesdropper will still be detectable in a similar manner. Now, consider the case where one of the participants of the protocol (say Bob)

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2310-434: The receivers' particles, but it is crucial that no measurements be made during this reconstruction process or any superposition within the quantum state will collapse. The security of QSS relies upon the no-cloning theorem to protect against possible eavesdroppers as well as dishonest users. This section adopts the two-particle entanglement protocol very briefly mentioned above. QSS promises security against eavesdropping in

2365-420: The reliability of the measurement. Orthogonal testing thus can be viewed as "cross-checking" of results, and the "cross" notion corresponds to the etymologic origin of orthogonality . Orthogonal testing is often required as a part of a new drug application . In the field of system reliability orthogonal redundancy is that form of redundancy where the form of backup device or method is completely different from

2420-494: The same way as two-photon Bell tests , it can be shown that this setup violates a Bell-type inequality for three particles, where E ( α + β + γ ) {\displaystyle E(\alpha +\beta +\gamma )} is the expectation value for a coincidence measurement with phase shifter settings ( α , β , γ ) {\displaystyle (\alpha ,\beta ,\gamma )} . For this experiment,

2475-456: The scope, content, and purpose of the pieces of writing are entirely unrelated. In board games such as chess which feature a grid of squares, 'orthogonal' is used to mean "in the same row/'rank' or column/'file'". This is the counterpart to squares which are "diagonally adjacent". In the ancient Chinese board game Go a player can capture the stones of an opponent by occupying all orthogonally adjacent points. Stereo vinyl records encode both

2530-517: The secret is bounded by n /2 < k ≤ n . Consider for n ≥ 2 k , if a (( k , n )) threshold scheme is applied to two disjoint sets of k in n , then two independent copies of Alice's secret can be reconstructed. This of course would violate the no-cloning theorem and is why n must be less than 2k. As long as a (( k , n )) threshold scheme exists, a (( k , n -1)) threshold scheme can be constructed by simply discarding one share. This method can be repeated until k=n. The following outlines

2585-666: The sender be denoted as Alice and two receivers as Bob and Charlie. Alice's objective is to send each receiver a "share" of her secret key (really just a quantum state) in such a way that: Alice initiates the protocol by sharing with each of Bob and Charlie one particle from a GHZ triplet in the (standard) Z-basis, holding onto the third particle herself: where | 0 ⟩ {\displaystyle |\mathrm {0} \rangle } and | 1 ⟩ {\displaystyle |\mathrm {1} \rangle } are orthogonal modes in an arbitrary Hilbert space . After each participant measures their particle in

2640-491: The state | 0 ⟩ c + | 1 ⟩ c 2 {\displaystyle {\frac {|0\rangle _{c}+|1\rangle _{c}}{\sqrt {2}}}} and if Alice and Bob have anticorrelated results then Charlie has the state | 0 ⟩ c − | 1 ⟩ c 2 {\displaystyle {\frac {|0\rangle _{c}-|1\rangle _{c}}{\sqrt {2}}}} . It

2695-503: The state she sent him and half of the time this will be the correct detection, but only because the state from the wrong basis is an equal superposition of the two states in the correct basis. Thus, half of the time that Eve measures in the wrong basis and therefore sends the incorrect state, Bob will measure the wrong state. This intervention on Eve's part leads to causing an error in the protocol on an extra 25% of trials. Therefore, with enough measurements, it will be nearly impossible to miss

2750-591: The technical effect produced by a component of a system neither creates nor propagates side effects to other components of the system. Typically this is achieved through the separation of concerns and encapsulation , and it is essential for feasible and compact designs of complex systems. The emergent behavior of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e., non-orthogonal design of modules and interfaces. Orthogonality reduces testing and development time because it

2805-541: The theory to make use of quantum states for establishing a secure key that could be used to transmit the secret via classical data. In the years following, more work was done to extend the theory to transmitting quantum information as the secret, rather than just using quantum states for establishing the cryptographic key. QSS has been proposed for being used in quantum money as well as for joint checking accounts , quantum networking , and distributed quantum computing , among other applications. This example follows

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2860-399: The third correlated photon being the pump photon. The experimental setup works as follows: Using | X ⟩ i , | Y ⟩ j {\displaystyle |\mathrm {X} \rangle _{i},|\mathrm {Y} \rangle _{j}} where X and Y are either 'S' for short path or 'L' for long path and i and j are one of 'A', 'B', or 'C' to label

2915-510: The time will he be able to extract useful information. The other half of the time the results must be discarded. Additionally, from the table one can see that Charlie has no way of determining who measured what, only if the results of Alice and Bob were correlated or anticorrelated. Thus the only way for Charlie to figure out Alice's measurement is by working together with Bob and sharing their results. In doing so, they can extract Alice's results for every measurement and use this information to create

2970-488: The title QSS . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=QSS&oldid=1101056485 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Quantum Secret Sharing The method of secret sharing consists of

3025-536: Was more challenging to implement because of the difficulties in producing three-particle correlations via either down-conversion processes with χ 3 {\displaystyle \chi ^{3}} nonlinearities or three-photon positronium annihilation, both of which are rare events. Instead, the original experiment was performed via the two-particle scheme using a standard χ 2 {\displaystyle \chi ^{2}} spontaneous parametric down-conversion (SPDC) process with

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